Master File

<<<<<<< HEAD ======= >>>>>>> 8e6f61bca4894b586983e20a3e14b1b8a049b903

User Inputs

output.var = params$output.var 

transform.abs = FALSE
log.pred = params$log.pred
norm.pred = FALSE
algo.forward.caret = params$algo.forward.caret
algo.backward.caret = params$algo.backward.caret
algo.stepwise.caret = params$algo.stepwise.caret
algo.LASSO.caret = params$algo.LASSO.caret
algo.LARS.caret = params$algo.LARS.caret
message("Parameters used for training/prediction: ")

## Parameters used for training/prediction:

str(params)

## List of 7
##  $ output.var         : chr "y3"
##  $ log.pred           : logi TRUE
##  $ algo.forward.caret : logi TRUE
##  $ algo.backward.caret: logi TRUE
##  $ algo.stepwise.caret: logi TRUE
##  $ algo.LASSO.caret   : logi TRUE
##  $ algo.LARS.caret    : logi TRUE

# Setup Labels
output.var.tr = if (log.pred == TRUE)  paste0(output.var,'.log') else  output.var.tr = output.var

Loading Data

feat  = read.csv('../../Data/features_highprec.csv')
labels = read.csv('../../Data/labels.csv')
predictors = names(dplyr::select(feat,-JobName))
data.ori = inner_join(feat,labels,by='JobName')
#data.ori = inner_join(feat,select_at(labels,c('JobName',output.var)),by='JobName')

Data validation

cc  = complete.cases(data.ori)
data.notComplete = data.ori[! cc,]
data = data.ori[cc,] %>% select_at(c(predictors,output.var,'JobName'))
message('Original cases: ',nrow(data.ori))

## Original cases: 10000

message('Non-Complete cases: ',nrow(data.notComplete))

## Non-Complete cases: 3020

message('Complete cases: ',nrow(data))

## Complete cases: 6980

summary(dplyr::select_at(data,c('JobName',output.var)))

##       JobName           y3        
##  Job_00001:   1   Min.   : 95.91  
##  Job_00002:   1   1st Qu.:118.29  
##  Job_00003:   1   Median :124.03  
##  Job_00004:   1   Mean   :125.40  
##  Job_00007:   1   3rd Qu.:131.06  
##  Job_00008:   1   Max.   :193.73  
##  (Other)  :6974

Output Variable

The Output Variable y3 shows right skewness, so will proceed with a log transformation

Histogram

df=gather(select_at(data,output.var))
ggplot(df, aes(x=value)) + 
  geom_histogram(aes(y=..density..),bins = 50,fill='light blue') + 
  geom_density() 

  #stat_function(fun = dnorm, n = 100, args = list(mean = mean(df$value), sd = sd(df$value)))  

QQPlot

ggplot(gather(select_at(data,output.var)), aes(sample=value)) + 
  stat_qq() + 
  facet_wrap(~key, scales = 'free',ncol=4)

Trasformation of Output Variable from y3 to y3.log

if(log.pred==TRUE) data[[output.var.tr]] = log(data[[output.var]],10) else
  data[[output.var.tr]] = data[[output.var]]
df=gather(select_at(data,c(output.var,output.var.tr)))
ggplot(df, aes(value)) + 
  geom_histogram(aes(y=..density..),bins = 50,fill='light blue') + 
  geom_density() + 
  # stat_function(fun = dnorm, n = 100, args = list(mean = mean(df$value), sd = sd(df$value)))  
  facet_wrap(~key, scales = 'free',ncol=2)

ggplot(gather(select_at(data,c(output.var,output.var.tr))), aes(sample=value)) + 
  stat_qq() + 
  facet_wrap(~key, scales = 'free',ncol=4)

Best Normalizator y3

Normalization of y3 using bestNormalize package. (suggested orderNorm) This is cool, but I think is too far for the objective of the project

t=bestNormalize::bestNormalize(data[[output.var]])

t

## Best Normalizing transformation with 6980 Observations
##  Estimated Normality Statistics (Pearson P / df, lower => more normal):
##  - No transform: 2.9491 
##  - Box-Cox: 1.4149 
##  - Log_b(x+a): 1.9707 
##  - sqrt(x+a): 2.385 
##  - exp(x): 749.5512 
##  - arcsinh(x): 1.9705 
##  - Yeo-Johnson: 1.1284 
##  - orderNorm: 1.0815 
## Estimation method: Out-of-sample via CV with 10 folds and 5 repeats
##  
## Based off these, bestNormalize chose:
## orderNorm Transformation with 6980 nonmissing obs and no ties 
##  - Original quantiles:
##      0%     25%     50%     75%    100% 
##  95.913 118.289 124.030 131.059 193.726

qqnorm(data[[output.var]])

qqnorm(predict(t))

orderNorm() is a rank-based procedure by which the values of a vector are mapped to their percentile, which is then mapped to the same percentile of the normal distribution. Without the presence of ties, this essentially guarantees that the transformation leads to a uniform distribution

Predictors

All predictors show a Fat-Tail situation, where the two tails are very tall, and a low distribution around the mean. The orderNorm transformation can help (see [Best Normalizator] section)

Interesting Predictors

Histograms

cols = c('x11','x18','stat98','x7','stat110')
df=gather(select_at(data,cols))
ggplot(df, aes(value)) + 
  geom_histogram(aes(y=..density..),bins = 50,fill='light blue') + 
  geom_density() + 
  # stat_function(fun = dnorm, n = 100, args = list(mean = mean(df$value), sd = sd(df$value)))  
  facet_wrap(~key, scales = 'free',ncol=3)

# ggplot(gather(select_at(data,cols)), aes(sample=value)) + 
#   stat_qq()+
#   facet_wrap(~key, scales = 'free',ncol=2)

lapply(select_at(data,cols),summary)

## $x11
##      Min.   1st Qu.    Median      Mean   3rd Qu.      Max. 
## 9.000e-08 9.494e-08 1.001e-07 1.001e-07 1.052e-07 1.100e-07 
## 
## $x18
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   1.500   3.147   4.769   4.772   6.418   7.999 
## 
## $stat98
##      Min.   1st Qu.    Median      Mean   3rd Qu.      Max. 
## -2.998619 -1.551882 -0.015993 -0.005946  1.528405  2.999499 
## 
## $x7
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   0.700   1.266   1.854   1.852   2.446   3.000 
## 
## $stat110
##      Min.   1st Qu.    Median      Mean   3rd Qu.      Max. 
## -2.999543 -1.496865 -0.002193 -0.004129  1.504273  2.999563

Scatter plot vs. output variable **y3.log

d = gather(dplyr::select_at(data,c(cols,output.var.tr)),key=target,value=value,-!!output.var.tr)
ggplot(data=d, aes_string(x='value',y=output.var.tr)) + 
  geom_point(color='light green',alpha=0.5) + 
  geom_smooth() + 
  facet_wrap(~target, scales = 'free',ncol=3)

## `geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'

All Predictors

Histograms

All indicators have a strong indication of Fat-Tails

df=gather(select_at(data,predictors))
ggplot(df, aes(value)) + 
  geom_histogram(aes(y=..density..),bins = 50,fill='light blue') + 
  geom_density() + 
  # stat_function(fun = dnorm, n = 100, args = list(mean = mean(df$value), sd = sd(df$value)))  
  facet_wrap(~key, scales = 'free',ncol=4)

Correlations

With Output Variable

#chart.Correlation(select(data,-JobName),  pch=21)
t=as.data.frame(round(cor(dplyr::select(data,-one_of(output.var.tr,'JobName'))
                          ,select_at(data,output.var.tr)),4))  %>%
  rownames_to_column(var='variable') %>% filter(variable != !!output.var) %>% arrange(-y3.log)
#DT::datatable(t)
message("Top Positive")

## Top Positive

kable(head(arrange(t,desc(y3.log)),20))

variable	y3.log
x18	0.3120
x7	0.2091
stat98	0.1784
x9	0.1127
x17	0.0611
x16	0.0489
x10	0.0472
x21	0.0412
x11	0.0322
x8	0.0318
stat156	0.0287
stat23	0.0234
stat100	0.0206
stat144	0.0203
stat59	0.0202
stat60	0.0199
stat195	0.0199
stat141	0.0194
stat73	0.0192
stat197	0.0185

message("Top Negative")

## Top Negative

kable(head(arrange(t,y3.log),20))

variable	y3.log
stat110	-0.1594
x4	-0.0603
stat13	-0.0345
stat41	-0.0345
stat14	-0.0317
stat149	-0.0309
stat113	-0.0279
stat4	-0.0248
stat106	-0.0236
stat146	-0.0236
stat186	-0.0217
stat91	-0.0210
stat214	-0.0209
stat5	-0.0207
stat22	-0.0202
stat39	-0.0202
stat175	-0.0194
stat187	-0.0193
stat128	-0.0192
stat37	-0.0191

Between All Variables

#chart.Correlation(select(data,-JobName),  pch=21)
t=as.data.frame(round(cor(dplyr::select(data,-one_of('JobName'))),4))
#DT::datatable(t,options=list(scrollX=T))
message("Showing only 10 variables")

## Showing only 10 variables

kable(t[1:10,1:10])

	x1	x2	x3	x4	x5	x6	x7	x8	x9	x10
x1	1.0000	0.0034	-0.0028	0.0085	0.0068	0.0159	0.0264	-0.0012	0.0142	0.0013
x2	0.0034	1.0000	-0.0057	0.0004	-0.0094	-0.0101	0.0089	0.0078	0.0049	-0.0214
x3	-0.0028	-0.0057	1.0000	0.0029	0.0046	0.0006	-0.0105	-0.0002	0.0167	-0.0137
x4	0.0085	0.0004	0.0029	1.0000	-0.0059	0.0104	0.0098	0.0053	0.0061	-0.0023
x5	0.0068	-0.0094	0.0046	-0.0059	1.0000	0.0016	-0.0027	0.0081	0.0259	-0.0081
x6	0.0159	-0.0101	0.0006	0.0104	0.0016	1.0000	0.0200	-0.0157	0.0117	-0.0072
x7	0.0264	0.0089	-0.0105	0.0098	-0.0027	0.0200	1.0000	-0.0018	-0.0069	-0.0221
x8	-0.0012	0.0078	-0.0002	0.0053	0.0081	-0.0157	-0.0018	1.0000	0.0142	-0.0004
x9	0.0142	0.0049	0.0167	0.0061	0.0259	0.0117	-0.0069	0.0142	1.0000	0.0149
x10	0.0013	-0.0214	-0.0137	-0.0023	-0.0081	-0.0072	-0.0221	-0.0004	0.0149	1.0000

Scatter Plots with Output Variable

Scatter plots with all predictors and the output variable (y3.log)

d = gather(dplyr::select_at(data,c(predictors,output.var.tr)),key=target,value=value,-!!output.var.tr)
ggplot(data=d, aes_string(x='value',y=output.var.tr)) + 
  geom_point(color='light blue',alpha=0.5) + 
  geom_smooth() + 
  facet_wrap(~target, scales = 'free',ncol=4)

## `geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'

Multicollinearity - VIF

No Multicollinearity among predictors

Showing Top predictor by VIF Value

vifDF = usdm::vif(select_at(data,predictors)) %>% arrange(desc(VIF))
head(vifDF,15)

##    Variables      VIF
## 1    stat145 1.063704
## 2    stat142 1.062756
## 3    stat154 1.061976
## 4      stat1 1.059943
## 5      stat5 1.059813
## 6     stat93 1.059749
## 7     stat32 1.059513
## 8    stat156 1.059133
## 9     stat86 1.058644
## 10    stat14 1.058343
## 11    stat92 1.058224
## 12   stat150 1.058180
## 13   stat127 1.058168
## 14   stat200 1.058121
## 15   stat131 1.058006

Feature Eng

• Square Root transformation for x18

data.tr=data %>%
  mutate(x18.sqrt = sqrt(x18)) 
cols=c('x18','x18.sqrt')

Comparing Pre and Post Transformation Density Plots

# ggplot(gather(select_at(data.tr,cols)), aes(value)) + 
#   geom_histogram(aes(y=..density..),bins = 50,fill='light blue') + 
#   geom_density() + 
#   facet_wrap(~key, scales = 'free',ncol=4)

d = gather(dplyr::select_at(data.tr,c(cols,output.var.tr)),key=target,value=value,-!!output.var.tr)
ggplot(data=d, aes_string(x='value',y=output.var.tr)) + 
  geom_point(color='light blue',alpha=0.5) + 
  geom_smooth() + 
  facet_wrap(~target, scales = 'free',ncol=4)

## `geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'

#removing unwanted variables
data.tr=data.tr %>%
  dplyr::select_at(names(data.tr)[! names(data.tr) %in% c('x18','y3','JobName')])

data=data.tr
label.names=output.var.tr

Modeling

PCA

<<<<<<< HEAD

fullInteraction=1
=======
fullInteraction=TRUE
>>>>>>> 8e6f61bca4894b586983e20a3e14b1b8a049b903

pca.vars  = names(data)
pca.vars = pca.vars[!pca.vars %in% label.names]

if(fullInteraction){
  pca.formula =as.formula(paste0('~(',paste0(pca.vars, collapse ='+'),')^2'))
  pca.model = prcomp(formula=pca.formula,data=data[,pca.vars],center=T,scale.=T,retx = T)
  #saveRDS(pca.model,'pca.model.rds')
} else {
  pca.model =  prcomp(x=data[,pca.vars],center=T,scale.=T,retx = T)
}
targetCumVar = .8

pca.model$var = pca.model$sdev ^ 2 #eigenvalues
pca.model$pvar = pca.model$var / sum(pca.model$var)
pca.model$cumpvar = cumsum(pca.model$pvar )
pca.model$pcaSel = pca.model$cumpvar<=targetCumVar
pca.model$pcaSelCount = sum(pca.model$pcaSel)
pca.model$pcaSelTotVar = sum(pca.model$pvar[pca.model$pcaSel])
message(pca.model$pcaSelCount, " PCAs justify ",percent(targetCumVar)," of the total Variance. (",percent(pca.model$pcaSelTotVar),")")
## 3834 PCAs justify 80.0% of the total Variance. (80.0%)
plot(pca.model$var,xlab="Principal component", ylab="Proportion of variance explained",   type='b')
<<<<<<< HEAD

plot(cumsum(pca.model$pvar ),xlab="Principal component", ylab="Cumulative Proportion of variance explained", ylim=c(0,1), type='b')

screeplot(pca.model,npcs = pca.model$pcaSelCount)

screeplot(pca.model,npcs = pca.model$pcaSelCount,type='lines')

=======

plot(cumsum(pca.model$pvar ),xlab="Principal component", ylab="Cumulative Proportion of variance explained", ylim=c(0,1), type='b')

screeplot(pca.model,npcs = pca.model$pcaSelCount)

screeplot(pca.model,npcs = pca.model$pcaSelCount,type='lines')

>>>>>>> 8e6f61bca4894b586983e20a3e14b1b8a049b903
#summary(pca.model)
#pca.model$rotation
#creating dataset
data.pca = dplyr::select(data,!!label.names) %>% 
  dplyr::bind_cols(dplyr::select(as.data.frame(pca.model$x)
                                 ,!!colnames(pca.model$rotation)[pca.model$pcaSel])
  )

Train Test Split

data.pca = data[sample(nrow(data.pca)),] # randomly shuffle data
split = sample.split(data.pca[,label.names], SplitRatio = 0.8)

data.train = subset(data.pca, split == TRUE)
data.test = subset(data.pca, split == FALSE)

Common Functions

plot.diagnostics <-  function(model, train) {
  plot(model)
  
  residuals = resid(model) # Plotted above in plot(lm.out)
  r.standard = rstandard(model)
  r.student = rstudent(model)
  
  df = data.frame(x=predict(model,train),y=r.student)
  p=ggplot(data=df,aes(x=x,y=y)) +
    geom_point(color='blue',alpha=0.5,shape=20,size=2) +
    geom_hline(yintercept = 0,size=1)+
    ylab("Student Residuals") +
    xlab("Predicted Values")+
    ggtitle("Student Residual Plot")
  plot(p)
  
  df = data.frame(x=predict(model,train),y=r.standard)
  p=ggplot(data=df,aes(x=x,y=y)) +
    geom_point(color='blue',alpha=0.5,shape=20,size=2) +
    geom_hline(yintercept = c(-2,0,2),size=1)+
    ylab("Student Residuals") +
    xlab("Predicted Values")+
    ggtitle("Student Residual Plot")
  plot(p)
  # Histogram
  df=data.frame(r.student)
  p=ggplot(data=df,aes(r.student)) +
    geom_histogram(aes(y=..density..),bins = 50,fill='blue',alpha=0.6) + 
    stat_function(fun = dnorm, n = 100, args = list(mean = 0, sd = 1)) +
    ylab("Density")+
    xlab("Studentized Residuals")+
    ggtitle("Distribution of Studentized Residuals")
  plot(p)
  # http://www.stat.columbia.edu/~martin/W2024/R7.pdf
  # Influential plots
  inf.meas = influence.measures(model)
  # print (summary(inf.meas)) # too much data
  
  # Leverage plot
  lev = hat(model.matrix(model))
  df=tibble::rownames_to_column(as.data.frame(lev),'id')
  p=ggplot(data=df,aes(x=as.numeric(id),y=lev)) +
    geom_point(color='blue',alpha=0.5,shape=20,size=2) +
    ylab('Leverage - check') + 
    xlab('Index')
  plot(p)
  # Cook's Distance
  cd = cooks.distance(model)
  df=tibble::rownames_to_column(as.data.frame(cd),'id')
  p=ggplot(data=df,aes(x=as.numeric(id),y=cd)) +
    geom_point(color='blue',alpha=0.5,shape=20,size=2) +
    geom_text(data=filter(df,cd>15/nrow(train)),aes(label=id),check_overlap=T,size=3,vjust=-.5)+
    ylab('Cooks distances') + 
    geom_hline(yintercept = c(4/nrow(train),0),size=1)+
    xlab('Index')
  plot(p)
  print (paste("Number of data points that have Cook's D > 4/n: ", length(cd[cd > 4/nrow(train)]), sep = "")) 
  print (paste("Number of data points that have Cook's D > 1: ", length(cd[cd > 1]), sep = "")) 
  return(cd)
}

# function to set up random seeds
# Based on http://jaehyeon-kim.github.io/2015/05/Setup-Random-Seeds-on-Caret-Package.html 
setCaretSeeds <- function(method = "cv", numbers = 1, repeats = 1, tunes = NULL, seed = 1701) {
  #B is the number of resamples and integer vector of M (numbers + tune length if any)
  B <- if (method == "cv") numbers
  else if(method == "repeatedcv") numbers * repeats
  else NULL
  if(is.null(length)) {
    seeds <- NULL
  } else {
    set.seed(seed = seed)
    seeds <- vector(mode = "list", length = B)
    seeds <- lapply(seeds, function(x) sample.int(n = 1000000
                                                  , size = numbers + ifelse(is.null(tunes), 0, tunes)))
    seeds[[length(seeds) + 1]] <- sample.int(n = 1000000, size = 1)
  }
  # return seeds
  seeds
}



train.caret.glmselect = function(formula, data, method
                                 ,subopt = NULL, feature.names
                                 , train.control = NULL, tune.grid = NULL, pre.proc = NULL){
  
  if(is.null(train.control)){
    train.control <- trainControl(method = "cv"
                              ,number = 10
                              ,seeds = setCaretSeeds(method = "cv"
                                                     , numbers = 10
                                                     , seed = 1701)
                              ,search = "grid"
                              ,verboseIter = TRUE
                              ,allowParallel = TRUE
                              )
  }
  
  if(is.null(tune.grid)){
    if (method == 'leapForward' | method == 'leapBackward' | method == 'leapSeq'){
      tune.grid = data.frame(nvmax = 1:length(feature.names))
    }
    if (method == 'glmnet' && subopt == 'LASSO'){
      # Will only show 1 Lambda value during training, but that is OK
      # https://stackoverflow.com/questions/47526544/why-need-to-tune-lambda-with-carettrain-method-glmnet-and-cv-glmnet
      # Another option for LASSO is this: https://github.com/topepo/caret/blob/master/RegressionTests/Code/lasso.R
      lambda = 10^seq(-2,0, length =100)
      alpha = c(1)
      tune.grid = expand.grid(alpha = alpha,lambda = lambda)
    }
    if (method == 'lars'){
      # https://github.com/topepo/caret/blob/master/RegressionTests/Code/lars.R
      fraction = seq(0, 1, length = 100)
      tune.grid = expand.grid(fraction = fraction)
      pre.proc = c("center", "scale") 
    }
  }
  
  # http://sshaikh.org/2015/05/06/parallelize-machine-learning-in-r-with-multi-core-cpus/
  cl <- makeCluster(ceiling(detectCores()*0.85)) # use 75% of cores only, leave rest for other tasks
  registerDoParallel(cl)

  set.seed(1) 
  # note that the seed has to actually be set just before this function is called
  # settign is above just not ensure reproducibility for some reason
  model.caret <- caret::train(formula
                              , data = data
                              , method = method
                              , tuneGrid = tune.grid
                              , trControl = train.control
                              , preProc = pre.proc
                              )
  
  stopCluster(cl)
  registerDoSEQ() # register sequential engine in case you are not using this function anymore
  
  if (method == 'leapForward' | method == 'leapBackward' | method == 'leapSeq'){
    print("All models results")
    print(model.caret$results) # all model results
    print("Best Model")
    print(model.caret$bestTune) # best model
    model = model.caret$finalModel

    # Metrics Plot 
    dataPlot = model.caret$results %>%
      gather(key='metric',value='value',-nvmax) %>%
      dplyr::filter(metric %in% c('MAE','RMSE','Rsquared'))
    metricsPlot = ggplot(data=dataPlot,aes(x=nvmax,y=value) ) +
      geom_line(color='lightblue4') +
      geom_point(color='blue',alpha=0.7,size=.9) +
      facet_wrap(~metric,ncol=2,scales='free_y')+
      theme_light()
    plot(metricsPlot)
    
    # Residuals Plot
    # leap function does not support studentized residuals
    dataPlot=data.frame(pred=predict(model.caret,data),res=resid(model.caret))
    residPlot = ggplot(dataPlot,aes(x=pred,y=res)) +
      geom_point(color='light blue',alpha=0.7) +
      geom_smooth(method="lm")+
      theme_light()
    plot(residPlot)
   
    residHistogram = ggplot(dataPlot,aes(x=res)) +
      geom_histogram(aes(y=..density..),fill='light blue',alpha=1) +
      #geom_density(color='lightblue4') + 
      stat_function(fun = dnorm, n = 100, args = list(mean = mean(dataPlot$res)
                                                       , sd = sd(dataPlot$res)),color='lightblue4')  
      theme_light()
    plot(residHistogram)
    id = rownames(model.caret$bestTune)    
    # Provides the coefficients of the best model
    # regsubsets doens return a full model (see documentation of regsubset), so we need to recalcualte themodel
    # https://stackoverflow.com/questions/13063762/how-to-obtain-a-lm-object-from-regsubsets
    print("Coefficients of final model:")
    coefs <- coef(model, id=id)
    #calculate the model to the the coef intervals
    nams <- names(coefs)
    nams <- nams[!nams %in% "(Intercept)"]
    response <-  as.character(formula[[2]])
    form <- as.formula(paste(response, paste(nams, collapse = " + "), sep = " ~ "))
    mod <- lm(form, data = data)
    #coefs
    #coef(mod)
    print(car::Confint(mod))
    return(list(model = model,id = id, residPlot = residPlot, residHistogram=residHistogram
                ,modelLM=mod))
  }
  if (method == 'glmnet' && subopt == 'LASSO'){
    print(model.caret)
    print(plot(model.caret))
    print(model.caret$bestTune)
    
    print(model.caret$results)
    model=model.caret$finalModel
    # Metrics Plot 
    dataPlot = model.caret$results %>%
      gather(key='metric',value='value',-lambda) %>%
      dplyr::filter(metric %in% c('MAE','RMSE','Rsquared'))
    metricsPlot = ggplot(data=dataPlot,aes(x=lambda,y=value) ) +
      geom_line(color='lightblue4') +
      geom_point(color='blue',alpha=0.7,size=.9) +
      facet_wrap(~metric,ncol=2,scales='free_y')+
      theme_light()
    plot(metricsPlot)
    
    # Residuals Plot 
    dataPlot=data.frame(pred=predict(model.caret,data),res=resid(model.caret))
    residPlot = ggplot(dataPlot,aes(x=pred,y=res)) +
      geom_point(color='light blue',alpha=0.7) +
      geom_smooth(method="lm")+
      theme_light()
    plot(residPlot)

    residHistogram = ggplot(dataPlot,aes(x=res)) +
      geom_histogram(aes(y=..density..),fill='light blue',alpha=1) +
      #geom_density(color='lightblue4') +
      stat_function(fun = dnorm, n = 100, args = list(mean = mean(dataPlot$res)
                                                       , sd = sd(dataPlot$res)),color='lightblue4')  
      theme_light()
    plot(residHistogram)
    
    print("Coefficients") 
    #no interval for glmnet: https://stackoverflow.com/questions/39750965/confidence-intervals-for-ridge-regression
    t=coef(model,s=model.caret$bestTune$lambda)
    model.coef = t[which(t[,1]!=0),]
    print(as.data.frame(model.coef))
    id = NULL # not really needed but added for consistency
    return(list(model = model.caret,id = id, residPlot = residPlot, metricsPlot=metricsPlot ))
  }
  if (method == 'lars'){
    print(model.caret)
    print(plot(model.caret))
    print(model.caret$bestTune)
    
    # Metrics Plot
    dataPlot = model.caret$results %>%
        gather(key='metric',value='value',-fraction) %>%
      dplyr::filter(metric %in% c('MAE','RMSE','Rsquared'))
    metricsPlot = ggplot(data=dataPlot,aes(x=fraction,y=value) ) +
      geom_line(color='lightblue4') +
      geom_point(color='blue',alpha=0.7,size=.9) +
      facet_wrap(~metric,ncol=2,scales='free_y')+
      theme_light()
    plot(metricsPlot)
    
    # Residuals Plot
    dataPlot=data.frame(pred=predict(model.caret,data),res=resid(model.caret))
    residPlot = ggplot(dataPlot,aes(x=pred,y=res)) +
      geom_point(color='light blue',alpha=0.7) +
      geom_smooth(method="lm")+
      theme_light()
    plot(residPlot)

    residHistogram = ggplot(dataPlot,aes(x=res)) +
      geom_histogram(aes(y=..density..),fill='light blue',alpha=1) +
      #geom_density(color='lightblue4') + 
      stat_function(fun = dnorm, n = 100, args = list(mean = mean(dataPlot$res)
                                                       , sd = sd(dataPlot$res)),color='lightblue4')  
      theme_light()
    plot(residHistogram)
    
    print("Coefficients") 
    t=coef(model.caret$finalModel,s=model.caret$bestTune$fraction,mode='fraction')
    model.coef = t[which(t!=0)]
    print(model.coef)
    id = NULL # not really needed but added for consistency
    return(list(model = model.caret,id = id, residPlot = residPlot, residHistogram=residHistogram))
  }
}

# https://stackoverflow.com/questions/48265743/linear-model-subset-selection-goodness-of-fit-with-k-fold-cross-validation
# changed slightly since call[[2]] was just returning "formula" without actually returnign the value in formula
predict.regsubsets <- function(object, newdata, id, formula, ...) {
    #form <- as.formula(object$call[[2]])
    mat <- model.matrix(formula, newdata) # adds intercept and expands any interaction terms
    coefi <- coef(object, id = id)
    xvars <- names(coefi)
    return(mat[,xvars]%*%coefi)
}
  
test.model = function(model, test, level=0.95
                      ,draw.limits = FALSE, good = 0.1, ok = 0.15
                      ,method = NULL, subopt = NULL
                      ,id = NULL, formula, feature.names, label.names
                      ,transformation = NULL){
  ## if using caret for glm select equivalent functionality, 
  ## need to pass formula (full is ok as it will select subset of variables from there)
  if (is.null(method)){
    pred = predict(model, newdata=test, interval="confidence", level = level) 
  }
  
  if (method == 'leapForward' | method == 'leapBackward' | method == 'leapSeq'){
    pred = predict.regsubsets(model, newdata = test, id = id, formula = formula)
  }
  
  if (method == 'glmnet' && subopt == 'LASSO'){
    xtest = as.matrix(test[,feature.names]) 
    pred=as.data.frame(predict(model, xtest))
  }
  
  if (method == 'lars'){
    pred=as.data.frame(predict(model, newdata = test))
  }
    
  # Summary of predicted values
  print ("Summary of predicted values: ")
  print(summary(pred[,1]))

  test.mse = mean((test[,label.names]-pred[,1])^2)
  print (paste(method, subopt, "Test MSE:", test.mse, sep=" "))
  
  if(log.pred == TRUE || norm.pred == TRUE){
    # plot transformewd comparison first
    df=data.frame(x=test[,label.names],y=pred[,1])
    ggplot(df,aes(x=x,y=y)) +
      geom_point(color='blue',alpha=0.5,shape=20,size=2) +
      geom_abline(slope=1,intercept=0,color='black',size=1) +
      #scale_y_continuous(limits=c(min(df),max(df)))+
      xlab("Actual (Transformed)")+
      ylab("Predicted (Transformed)")
  }
    
  if (log.pred == FALSE && norm.pred == FALSE){
    x = test[,label.names]
    y = pred[,1]
  }
  if (log.pred == TRUE){
    x = 10^test[,label.names]
    y = 10^pred[,1]  
  }
  if (norm.pred == TRUE){
    x = predict(transformation, test[,label.names], inverse = TRUE)
    y = predict(transformation, pred[,1], inverse = TRUE)
  }

  df=data.frame(x,y)
  ggplot(df,aes(x,y)) +
    geom_point(color='blue',alpha=0.5,shape=20,size=2) +
    geom_abline(slope=c(1+good,1-good,1+ok,1-ok)
                ,intercept=rep(0,4),color=c('dark green','dark green','dark red','dark red'),size=1,alpha=0.8) +
    #scale_y_continuous(limits=c(min(df),max(df)))+
    xlab("Actual")+
    ylab("Predicted") 
    
 
}

Setup Formulae

n <- names(data.train)
 formula <- as.formula(paste(paste(n[n %in% label.names], collapse = " + ")
                             ," ~", paste(n[!n %in% label.names], collapse = " + "))) 

grand.mean.formula = as.formula(paste(paste(n[n %in% label.names], collapse = " + ")," ~ 1"))

print(formula)

## y3.log ~ x1 + x2 + x3 + x4 + x5 + x6 + x7 + x8 + x9 + x10 + x11 + 
##     x12 + x13 + x14 + x15 + x16 + x17 + x19 + x20 + x21 + x22 + 
##     x23 + stat1 + stat2 + stat3 + stat4 + stat5 + stat6 + stat7 + 
##     stat8 + stat9 + stat10 + stat11 + stat12 + stat13 + stat14 + 
##     stat15 + stat16 + stat17 + stat18 + stat19 + stat20 + stat21 + 
##     stat22 + stat23 + stat24 + stat25 + stat26 + stat27 + stat28 + 
##     stat29 + stat30 + stat31 + stat32 + stat33 + stat34 + stat35 + 
##     stat36 + stat37 + stat38 + stat39 + stat40 + stat41 + stat42 + 
##     stat43 + stat44 + stat45 + stat46 + stat47 + stat48 + stat49 + 
##     stat50 + stat51 + stat52 + stat53 + stat54 + stat55 + stat56 + 
##     stat57 + stat58 + stat59 + stat60 + stat61 + stat62 + stat63 + 
##     stat64 + stat65 + stat66 + stat67 + stat68 + stat69 + stat70 + 
##     stat71 + stat72 + stat73 + stat74 + stat75 + stat76 + stat77 + 
##     stat78 + stat79 + stat80 + stat81 + stat82 + stat83 + stat84 + 
##     stat85 + stat86 + stat87 + stat88 + stat89 + stat90 + stat91 + 
##     stat92 + stat93 + stat94 + stat95 + stat96 + stat97 + stat98 + 
##     stat99 + stat100 + stat101 + stat102 + stat103 + stat104 + 
##     stat105 + stat106 + stat107 + stat108 + stat109 + stat110 + 
##     stat111 + stat112 + stat113 + stat114 + stat115 + stat116 + 
##     stat117 + stat118 + stat119 + stat120 + stat121 + stat122 + 
##     stat123 + stat124 + stat125 + stat126 + stat127 + stat128 + 
##     stat129 + stat130 + stat131 + stat132 + stat133 + stat134 + 
##     stat135 + stat136 + stat137 + stat138 + stat139 + stat140 + 
##     stat141 + stat142 + stat143 + stat144 + stat145 + stat146 + 
##     stat147 + stat148 + stat149 + stat150 + stat151 + stat152 + 
##     stat153 + stat154 + stat155 + stat156 + stat157 + stat158 + 
##     stat159 + stat160 + stat161 + stat162 + stat163 + stat164 + 
##     stat165 + stat166 + stat167 + stat168 + stat169 + stat170 + 
##     stat171 + stat172 + stat173 + stat174 + stat175 + stat176 + 
##     stat177 + stat178 + stat179 + stat180 + stat181 + stat182 + 
##     stat183 + stat184 + stat185 + stat186 + stat187 + stat188 + 
##     stat189 + stat190 + stat191 + stat192 + stat193 + stat194 + 
##     stat195 + stat196 + stat197 + stat198 + stat199 + stat200 + 
##     stat201 + stat202 + stat203 + stat204 + stat205 + stat206 + 
##     stat207 + stat208 + stat209 + stat210 + stat211 + stat212 + 
##     stat213 + stat214 + stat215 + stat216 + stat217 + x18.sqrt

print(grand.mean.formula)

## y3.log ~ 1

# Update feature.names because we may have transformed some features
feature.names = n[!n %in% label.names]

Full Model

model.full = lm(formula , data.train)
summary(model.full)

## 
## Call:
## lm(formula = formula, data = data.train)
## 
## Residuals:
##       Min        1Q    Median        3Q       Max 
<<<<<<< HEAD
## -0.087823 -0.020936 -0.004818  0.016147  0.188961 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  1.975e+00  9.630e-03 205.059  < 2e-16 ***
## x1          -2.387e-04  6.596e-04  -0.362 0.717442    
## x2           1.606e-04  4.231e-04   0.380 0.704263    
## x3          -1.249e-05  1.156e-04  -0.108 0.913983    
## x4          -4.397e-05  9.085e-06  -4.841 1.33e-06 ***
## x5           5.205e-04  2.971e-04   1.752 0.079877 .  
## x6           4.011e-04  6.033e-04   0.665 0.506146    
## x7           1.135e-02  6.462e-04  17.560  < 2e-16 ***
## x8           4.261e-04  1.498e-04   2.844 0.004470 ** 
## x9           3.307e-03  3.346e-04   9.886  < 2e-16 ***
## x10          1.198e-03  3.115e-04   3.846 0.000121 ***
## x11          1.625e+05  7.442e+04   2.184 0.028998 *  
## x12         -1.228e-04  1.901e-04  -0.646 0.518362    
## x13          6.745e-05  7.560e-05   0.892 0.372311    
## x14         -3.510e-04  3.264e-04  -1.075 0.282313    
## x15          9.911e-05  3.096e-04   0.320 0.748911    
## x16          6.822e-04  2.160e-04   3.159 0.001592 ** 
## x17          1.525e-03  3.280e-04   4.651 3.38e-06 ***
## x19          2.325e-04  1.678e-04   1.385 0.166009    
## x20         -2.204e-04  1.160e-03  -0.190 0.849337    
## x21          1.265e-04  4.276e-05   2.959 0.003100 ** 
## x22         -3.904e-04  3.473e-04  -1.124 0.261074    
## x23         -1.925e-04  3.305e-04  -0.583 0.560216    
## stat1       -2.356e-04  2.493e-04  -0.945 0.344825    
## stat2        8.538e-05  2.494e-04   0.342 0.732048    
## stat3        3.428e-04  2.503e-04   1.370 0.170841    
## stat4       -3.667e-04  2.534e-04  -1.447 0.148028    
## stat5        6.690e-06  2.526e-04   0.026 0.978876    
## stat6       -1.419e-04  2.506e-04  -0.566 0.571200    
## stat7       -6.248e-05  2.522e-04  -0.248 0.804295    
## stat8        2.401e-04  2.502e-04   0.960 0.337282    
## stat9        7.159e-05  2.508e-04   0.285 0.775333    
## stat10      -2.328e-04  2.513e-04  -0.926 0.354271    
## stat11      -1.457e-04  2.532e-04  -0.575 0.565003    
## stat12       3.127e-04  2.504e-04   1.248 0.211914    
## stat13      -5.756e-04  2.494e-04  -2.308 0.021032 *  
## stat14      -8.059e-04  2.486e-04  -3.241 0.001197 ** 
## stat15      -3.954e-04  2.492e-04  -1.587 0.112575    
## stat16       7.597e-05  2.503e-04   0.304 0.761505    
## stat17      -1.442e-04  2.490e-04  -0.579 0.562526    
## stat18      -2.127e-04  2.498e-04  -0.852 0.394450    
## stat19       1.500e-04  2.496e-04   0.601 0.547867    
## stat20      -9.038e-05  2.501e-04  -0.361 0.717867    
## stat21      -2.529e-05  2.517e-04  -0.100 0.919987    
## stat22      -6.685e-04  2.505e-04  -2.668 0.007649 ** 
## stat23       7.748e-04  2.502e-04   3.097 0.001967 ** 
## stat24      -7.147e-04  2.512e-04  -2.846 0.004450 ** 
## stat25      -4.518e-04  2.493e-04  -1.812 0.069987 .  
## stat26      -3.711e-04  2.501e-04  -1.484 0.137993    
## stat27       2.482e-04  2.508e-04   0.990 0.322415    
## stat28      -6.528e-06  2.505e-04  -0.026 0.979213    
## stat29       2.612e-04  2.528e-04   1.033 0.301477    
## stat30       3.596e-04  2.526e-04   1.424 0.154514    
## stat31      -4.958e-05  2.531e-04  -0.196 0.844666    
## stat32       3.993e-04  2.523e-04   1.583 0.113468    
## stat33      -1.760e-04  2.497e-04  -0.705 0.480846    
## stat34      -4.333e-05  2.498e-04  -0.173 0.862298    
## stat35      -3.934e-04  2.514e-04  -1.565 0.117753    
## stat36      -3.094e-05  2.481e-04  -0.125 0.900793    
## stat37      -4.522e-04  2.526e-04  -1.790 0.073433 .  
## stat38       4.082e-04  2.513e-04   1.624 0.104389    
## stat39      -3.480e-04  2.494e-04  -1.395 0.163012    
## stat40      -2.057e-05  2.511e-04  -0.082 0.934696    
## stat41      -3.916e-04  2.492e-04  -1.572 0.116104    
## stat42      -7.757e-05  2.499e-04  -0.310 0.756286    
## stat43      -3.372e-04  2.507e-04  -1.345 0.178706    
## stat44       5.649e-05  2.525e-04   0.224 0.823011    
## stat45      -3.576e-04  2.488e-04  -1.437 0.150661    
## stat46       3.615e-04  2.506e-04   1.442 0.149294    
## stat47       2.193e-04  2.521e-04   0.870 0.384430    
## stat48       1.328e-04  2.511e-04   0.529 0.596912    
## stat49      -1.785e-05  2.485e-04  -0.072 0.942753    
## stat50       4.444e-04  2.485e-04   1.788 0.073806 .  
## stat51       4.969e-04  2.510e-04   1.980 0.047748 *  
## stat52      -2.364e-05  2.516e-04  -0.094 0.925118    
## stat53      -2.170e-04  2.526e-04  -0.859 0.390389    
## stat54      -4.232e-04  2.515e-04  -1.682 0.092545 .  
## stat55       3.422e-04  2.488e-04   1.376 0.169030    
## stat56      -4.455e-05  2.523e-04  -0.177 0.859827    
## stat57      -5.070e-05  2.473e-04  -0.205 0.837594    
## stat58       1.508e-04  2.493e-04   0.605 0.545353    
## stat59       3.180e-04  2.521e-04   1.261 0.207234    
## stat60       4.982e-04  2.512e-04   1.983 0.047400 *  
## stat61      -1.615e-05  2.520e-04  -0.064 0.948899    
## stat62       1.236e-04  2.498e-04   0.495 0.620865    
## stat63       4.348e-04  2.525e-04   1.722 0.085120 .  
## stat64      -1.120e-04  2.505e-04  -0.447 0.654842    
## stat65      -4.327e-04  2.516e-04  -1.720 0.085482 .  
## stat66       1.192e-04  2.541e-04   0.469 0.638963    
## stat67       1.168e-04  2.518e-04   0.464 0.642762    
## stat68      -7.627e-05  2.514e-04  -0.303 0.761590    
## stat69      -1.993e-04  2.498e-04  -0.798 0.425051    
## stat70       2.298e-04  2.494e-04   0.921 0.356952    
## stat71       1.194e-04  2.500e-04   0.478 0.632913    
## stat72       1.345e-04  2.513e-04   0.535 0.592373    
## stat73       3.373e-04  2.507e-04   1.346 0.178501    
## stat74      -2.392e-04  2.533e-04  -0.944 0.345169    
## stat75      -3.282e-04  2.531e-04  -1.297 0.194725    
## stat76       2.726e-04  2.511e-04   1.085 0.277837    
## stat77       7.751e-05  2.506e-04   0.309 0.757155    
## stat78      -1.470e-04  2.510e-04  -0.586 0.558200    
## stat79      -1.147e-04  2.516e-04  -0.456 0.648475    
## stat80       2.112e-04  2.514e-04   0.840 0.400866    
## stat81       2.846e-04  2.509e-04   1.134 0.256643    
## stat82       1.995e-04  2.493e-04   0.800 0.423649    
## stat83      -1.159e-04  2.501e-04  -0.463 0.643117    
## stat84       2.899e-05  2.504e-04   0.116 0.907838    
## stat85       2.604e-04  2.517e-04   1.034 0.300974    
## stat86       2.713e-04  2.502e-04   1.084 0.278446    
## stat87      -4.699e-04  2.511e-04  -1.872 0.061301 .  
## stat88      -6.743e-05  2.491e-04  -0.271 0.786634    
## stat89      -1.364e-04  2.478e-04  -0.550 0.582116    
## stat90      -8.980e-05  2.509e-04  -0.358 0.720412    
## stat91      -3.304e-04  2.487e-04  -1.328 0.184126    
## stat92      -4.869e-04  2.521e-04  -1.932 0.053448 .  
## stat93       9.592e-06  2.533e-04   0.038 0.969795    
## stat94      -3.932e-04  2.520e-04  -1.560 0.118754    
## stat95      -4.614e-04  2.510e-04  -1.838 0.066051 .  
## stat96      -2.965e-04  2.494e-04  -1.189 0.234609    
## stat97       2.322e-04  2.477e-04   0.937 0.348573    
## stat98       3.502e-03  2.466e-04  14.204  < 2e-16 ***
## stat99       3.843e-04  2.523e-04   1.524 0.127673    
## stat100      6.738e-04  2.501e-04   2.694 0.007087 ** 
## stat101     -1.245e-04  2.536e-04  -0.491 0.623634    
## stat102     -2.460e-04  2.530e-04  -0.973 0.330805    
## stat103     -2.711e-04  2.537e-04  -1.069 0.285200    
## stat104     -3.447e-04  2.508e-04  -1.374 0.169358    
## stat105      7.012e-05  2.495e-04   0.281 0.778671    
## stat106     -4.950e-04  2.501e-04  -1.979 0.047864 *  
## stat107     -4.943e-05  2.489e-04  -0.199 0.842586    
## stat108     -9.507e-05  2.508e-04  -0.379 0.704657    
## stat109     -6.885e-05  2.498e-04  -0.276 0.782852    
## stat110     -3.408e-03  2.505e-04 -13.605  < 2e-16 ***
## stat111     -1.479e-04  2.495e-04  -0.593 0.553439    
## stat112     -3.040e-04  2.522e-04  -1.205 0.228094    
## stat113     -2.801e-04  2.520e-04  -1.111 0.266497    
## stat114     -6.692e-05  2.491e-04  -0.269 0.788185    
## stat115      3.161e-04  2.496e-04   1.266 0.205510    
## stat116      2.466e-04  2.517e-04   0.980 0.327154    
## stat117      2.054e-04  2.505e-04   0.820 0.412221    
## stat118     -2.001e-04  2.478e-04  -0.807 0.419581    
## stat119      9.629e-05  2.486e-04   0.387 0.698517    
## stat120      8.546e-05  2.492e-04   0.343 0.731690    
## stat121     -1.911e-04  2.510e-04  -0.761 0.446484    
## stat122     -5.084e-05  2.484e-04  -0.205 0.837826    
## stat123      2.107e-04  2.540e-04   0.830 0.406858    
## stat124     -1.455e-04  2.515e-04  -0.579 0.562766    
## stat125      4.498e-05  2.519e-04   0.179 0.858296    
## stat126      1.123e-04  2.507e-04   0.448 0.654156    
## stat127      1.111e-04  2.498e-04   0.445 0.656350    
## stat128     -6.007e-05  2.493e-04  -0.241 0.809644    
## stat129      1.943e-04  2.493e-04   0.779 0.435840    
## stat130      3.403e-04  2.522e-04   1.349 0.177260    
## stat131      1.753e-04  2.517e-04   0.696 0.486304    
## stat132     -7.555e-06  2.496e-04  -0.030 0.975856    
## stat133      2.194e-04  2.508e-04   0.875 0.381821    
## stat134     -2.577e-04  2.489e-04  -1.035 0.300513    
## stat135      9.441e-05  2.505e-04   0.377 0.706302    
## stat136     -7.168e-05  2.523e-04  -0.284 0.776362    
## stat137      1.010e-04  2.482e-04   0.407 0.684121    
## stat138      8.468e-05  2.505e-04   0.338 0.735306    
## stat139      3.312e-05  2.512e-04   0.132 0.895129    
## stat140     -2.539e-04  2.490e-04  -1.020 0.307895    
## stat141      2.413e-04  2.499e-04   0.966 0.334211    
## stat142     -1.488e-04  2.533e-04  -0.588 0.556832    
## stat143      2.042e-04  2.500e-04   0.817 0.414195    
## stat144      5.299e-04  2.496e-04   2.123 0.033818 *  
## stat145     -1.074e-04  2.538e-04  -0.423 0.672076    
## stat146     -4.488e-04  2.521e-04  -1.780 0.075093 .  
## stat147     -4.115e-04  2.518e-04  -1.634 0.102295    
## stat148     -2.412e-04  2.487e-04  -0.970 0.332207    
## stat149     -5.992e-04  2.519e-04  -2.379 0.017388 *  
## stat150     -8.703e-05  2.522e-04  -0.345 0.730063    
## stat151     -1.633e-04  2.526e-04  -0.646 0.518125    
## stat152     -3.056e-04  2.488e-04  -1.229 0.219303    
## stat153      5.868e-06  2.538e-04   0.023 0.981557    
## stat154     -9.471e-05  2.534e-04  -0.374 0.708583    
## stat155     -1.421e-04  2.481e-04  -0.573 0.566926    
## stat156      4.839e-04  2.535e-04   1.909 0.056335 .  
## stat157      2.549e-05  2.488e-04   0.102 0.918407    
## stat158      5.433e-06  2.534e-04   0.021 0.982894    
## stat159      3.627e-04  2.507e-04   1.447 0.147940    
## stat160     -1.260e-04  2.514e-04  -0.501 0.616222    
## stat161      2.147e-04  2.511e-04   0.855 0.392577    
## stat162      1.679e-05  2.495e-04   0.067 0.946350    
## stat163      6.746e-05  2.531e-04   0.266 0.789879    
## stat164      9.088e-05  2.541e-04   0.358 0.720555    
## stat165      6.278e-05  2.489e-04   0.252 0.800857    
## stat166     -2.529e-04  2.482e-04  -1.019 0.308170    
## stat167     -2.202e-04  2.493e-04  -0.883 0.377174    
## stat168     -2.163e-04  2.499e-04  -0.866 0.386776    
## stat169      5.172e-05  2.508e-04   0.206 0.836619    
## stat170     -4.443e-04  2.512e-04  -1.768 0.077039 .  
## stat171     -3.331e-05  2.520e-04  -0.132 0.894862    
## stat172      4.010e-04  2.490e-04   1.610 0.107353    
## stat173     -3.757e-04  2.516e-04  -1.494 0.135363    
## stat174      1.268e-05  2.506e-04   0.051 0.959643    
## stat175     -4.957e-04  2.507e-04  -1.978 0.048026 *  
## stat176      2.491e-04  2.511e-04   0.992 0.321190    
## stat177     -3.028e-05  2.525e-04  -0.120 0.904553    
## stat178     -1.761e-04  2.548e-04  -0.691 0.489447    
## stat179     -6.063e-06  2.485e-04  -0.024 0.980539    
## stat180     -2.505e-04  2.486e-04  -1.008 0.313618    
## stat181      2.090e-04  2.529e-04   0.826 0.408638    
## stat182      2.363e-04  2.523e-04   0.936 0.349083    
## stat183      1.453e-04  2.509e-04   0.579 0.562570    
## stat184     -1.816e-05  2.544e-04  -0.071 0.943087    
## stat185     -4.392e-04  2.478e-04  -1.772 0.076415 .  
## stat186     -1.832e-04  2.526e-04  -0.725 0.468297    
## stat187     -5.102e-04  2.505e-04  -2.037 0.041720 *  
## stat188     -1.755e-04  2.499e-04  -0.702 0.482592    
## stat189     -4.887e-05  2.511e-04  -0.195 0.845695    
## stat190      1.163e-04  2.491e-04   0.467 0.640759    
## stat191     -4.392e-04  2.504e-04  -1.754 0.079506 .  
## stat192      2.150e-04  2.532e-04   0.849 0.395970    
## stat193      1.595e-04  2.529e-04   0.630 0.528423    
## stat194      1.189e-04  2.493e-04   0.477 0.633499    
## stat195      2.354e-04  2.503e-04   0.941 0.346919    
## stat196     -2.817e-04  2.539e-04  -1.110 0.267257    
## stat197      2.144e-05  2.480e-04   0.086 0.931118    
## stat198     -2.001e-04  2.515e-04  -0.796 0.426248    
## stat199      3.489e-04  2.494e-04   1.399 0.161937    
## stat200     -2.205e-04  2.476e-04  -0.890 0.373276    
## stat201      5.049e-05  2.505e-04   0.202 0.840235    
## stat202     -2.250e-04  2.543e-04  -0.885 0.376329    
## stat203      6.231e-05  2.499e-04   0.249 0.803157    
## stat204     -4.822e-04  2.483e-04  -1.942 0.052136 .  
## stat205     -6.006e-05  2.492e-04  -0.241 0.809563    
## stat206     -1.047e-04  2.512e-04  -0.417 0.677022    
## stat207      3.507e-04  2.500e-04   1.403 0.160710    
## stat208     -9.681e-05  2.511e-04  -0.386 0.699863    
## stat209     -2.701e-04  2.490e-04  -1.085 0.278128    
## stat210     -2.866e-04  2.503e-04  -1.145 0.252266    
## stat211     -1.123e-04  2.503e-04  -0.449 0.653704    
## stat212      8.265e-05  2.504e-04   0.330 0.741371    
## stat213     -1.577e-04  2.525e-04  -0.624 0.532336    
## stat214     -3.493e-04  2.512e-04  -1.391 0.164384    
## stat215     -3.036e-05  2.502e-04  -0.121 0.903426    
## stat216     -1.871e-04  2.510e-04  -0.746 0.455968    
## stat217      3.134e-04  2.504e-04   1.251 0.210830    
## x18.sqrt     2.533e-02  9.591e-04  26.407  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.03173 on 5343 degrees of freedom
## Multiple R-squared:  0.2633, Adjusted R-squared:  0.2302 
## F-statistic: 7.958 on 240 and 5343 DF,  p-value: < 2.2e-16

cd.full = plot.diagnostics(model=model.full, train=data.train)

## [1] "Number of data points that have Cook's D > 4/n: 288"
=======
## -0.082957 -0.020817 -0.004661  0.016249  0.160450 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  1.967e+00  9.510e-03 206.834  < 2e-16 ***
## x1          -3.335e-04  6.533e-04  -0.510  0.60976    
## x2           3.317e-04  4.148e-04   0.800  0.42402    
## x3           5.063e-05  1.150e-04   0.440  0.65965    
## x4          -4.629e-05  8.995e-06  -5.146 2.76e-07 ***
## x5           1.793e-04  2.944e-04   0.609  0.54252    
## x6           1.391e-04  5.935e-04   0.234  0.81475    
## x7           1.104e-02  6.382e-04  17.300  < 2e-16 ***
## x8           4.382e-04  1.489e-04   2.944  0.00326 ** 
## x9           3.070e-03  3.306e-04   9.288  < 2e-16 ***
## x10          1.223e-03  3.082e-04   3.967 7.38e-05 ***
## x11          2.028e+05  7.358e+04   2.756  0.00586 ** 
## x12          1.078e-04  1.883e-04   0.573  0.56682    
## x13          3.925e-05  7.480e-05   0.525  0.59973    
## x14         -4.059e-04  3.243e-04  -1.252  0.21066    
## x15          1.204e-04  3.074e-04   0.392  0.69526    
## x16          1.021e-03  2.136e-04   4.780 1.80e-06 ***
## x17          1.858e-03  3.249e-04   5.718 1.14e-08 ***
## x19          1.350e-04  1.650e-04   0.818  0.41329    
## x20         -9.016e-04  1.151e-03  -0.783  0.43339    
## x21          1.082e-04  4.211e-05   2.568  0.01024 *  
## x22         -4.039e-04  3.467e-04  -1.165  0.24416    
## x23          2.964e-04  3.288e-04   0.901  0.36746    
## stat1       -1.579e-04  2.482e-04  -0.636  0.52475    
## stat2        1.423e-04  2.458e-04   0.579  0.56262    
## stat3        4.660e-04  2.484e-04   1.876  0.06073 .  
## stat4       -5.826e-04  2.492e-04  -2.338  0.01944 *  
## stat5       -1.030e-04  2.478e-04  -0.416  0.67778    
## stat6       -3.683e-05  2.481e-04  -0.148  0.88201    
## stat7       -1.612e-04  2.477e-04  -0.651  0.51522    
## stat8        2.214e-04  2.476e-04   0.894  0.37132    
## stat9       -2.382e-04  2.472e-04  -0.964  0.33524    
## stat10      -3.094e-04  2.481e-04  -1.247  0.21242    
## stat11      -9.168e-06  2.494e-04  -0.037  0.97067    
## stat12       2.652e-04  2.469e-04   1.074  0.28287    
## stat13      -6.644e-04  2.465e-04  -2.695  0.00705 ** 
## stat14      -7.599e-04  2.461e-04  -3.088  0.00202 ** 
## stat15      -2.643e-04  2.453e-04  -1.077  0.28138    
## stat16       8.957e-05  2.470e-04   0.363  0.71688    
## stat17       7.868e-06  2.458e-04   0.032  0.97446    
## stat18      -3.596e-04  2.479e-04  -1.451  0.14687    
## stat19       1.908e-05  2.467e-04   0.077  0.93836    
## stat20      -1.633e-04  2.487e-04  -0.657  0.51153    
## stat21      -3.260e-05  2.481e-04  -0.131  0.89549    
## stat22      -5.024e-04  2.488e-04  -2.020  0.04347 *  
## stat23       5.723e-04  2.474e-04   2.313  0.02075 *  
## stat24      -5.039e-04  2.483e-04  -2.030  0.04243 *  
## stat25      -6.027e-04  2.470e-04  -2.440  0.01474 *  
## stat26      -3.665e-04  2.469e-04  -1.484  0.13785    
## stat27       3.341e-05  2.483e-04   0.135  0.89298    
## stat28       5.207e-05  2.482e-04   0.210  0.83381    
## stat29       1.261e-04  2.494e-04   0.506  0.61317    
## stat30       2.392e-04  2.490e-04   0.961  0.33663    
## stat31       2.850e-05  2.496e-04   0.114  0.90910    
## stat32       2.199e-04  2.485e-04   0.885  0.37617    
## stat33      -4.095e-04  2.479e-04  -1.652  0.09863 .  
## stat34      -5.030e-05  2.472e-04  -0.203  0.83879    
## stat35      -3.877e-04  2.475e-04  -1.566  0.11730    
## stat36      -6.788e-05  2.456e-04  -0.276  0.78226    
## stat37      -2.305e-04  2.496e-04  -0.923  0.35586    
## stat38       3.643e-04  2.469e-04   1.476  0.14013    
## stat39      -2.239e-04  2.453e-04  -0.913  0.36134    
## stat40       4.679e-05  2.479e-04   0.189  0.85029    
## stat41      -6.082e-04  2.456e-04  -2.476  0.01332 *  
## stat42      -2.666e-04  2.462e-04  -1.083  0.27898    
## stat43      -1.332e-04  2.484e-04  -0.536  0.59188    
## stat44       5.118e-05  2.477e-04   0.207  0.83631    
## stat45      -4.018e-04  2.471e-04  -1.626  0.10395    
## stat46       2.959e-04  2.475e-04   1.195  0.23197    
## stat47      -1.944e-04  2.505e-04  -0.776  0.43771    
## stat48       3.389e-04  2.477e-04   1.369  0.17119    
## stat49       1.543e-04  2.466e-04   0.626  0.53153    
## stat50       2.624e-04  2.446e-04   1.073  0.28348    
## stat51       2.551e-04  2.476e-04   1.030  0.30298    
## stat52       1.664e-04  2.482e-04   0.671  0.50245    
## stat53      -1.117e-04  2.501e-04  -0.447  0.65505    
## stat54      -3.039e-04  2.490e-04  -1.220  0.22236    
## stat55       1.464e-04  2.454e-04   0.596  0.55093    
## stat56      -1.606e-04  2.481e-04  -0.647  0.51750    
## stat57      -1.618e-04  2.455e-04  -0.659  0.51001    
## stat58       1.598e-04  2.468e-04   0.647  0.51743    
## stat59       3.296e-04  2.471e-04   1.334  0.18235    
## stat60       4.065e-04  2.479e-04   1.640  0.10116    
## stat61      -1.628e-04  2.480e-04  -0.656  0.51163    
## stat62      -2.854e-04  2.469e-04  -1.156  0.24775    
## stat63      -1.058e-05  2.476e-04  -0.043  0.96591    
## stat64      -2.240e-04  2.461e-04  -0.910  0.36272    
## stat65      -6.171e-04  2.502e-04  -2.467  0.01367 *  
## stat66       8.904e-05  2.503e-04   0.356  0.72210    
## stat67       1.662e-04  2.492e-04   0.667  0.50490    
## stat68      -7.448e-05  2.488e-04  -0.299  0.76471    
## stat69      -1.223e-04  2.482e-04  -0.493  0.62238    
## stat70       4.184e-04  2.460e-04   1.701  0.08904 .  
## stat71      -9.952e-07  2.459e-04  -0.004  0.99677    
## stat72       1.125e-04  2.486e-04   0.453  0.65091    
## stat73       3.657e-04  2.488e-04   1.470  0.14155    
## stat74       1.594e-04  2.480e-04   0.643  0.52038    
## stat75      -1.272e-04  2.505e-04  -0.508  0.61164    
## stat76       5.902e-05  2.487e-04   0.237  0.81242    
## stat77      -1.312e-04  2.475e-04  -0.530  0.59606    
## stat78      -1.895e-04  2.473e-04  -0.766  0.44358    
## stat79      -1.691e-04  2.467e-04  -0.685  0.49316    
## stat80       1.611e-04  2.485e-04   0.648  0.51684    
## stat81       9.758e-05  2.479e-04   0.394  0.69383    
## stat82       1.953e-04  2.477e-04   0.788  0.43058    
## stat83       1.436e-04  2.477e-04   0.580  0.56202    
## stat84      -9.901e-05  2.476e-04  -0.400  0.68925    
## stat85       7.838e-05  2.472e-04   0.317  0.75123    
## stat86       4.018e-04  2.473e-04   1.625  0.10421    
## stat87      -1.974e-04  2.491e-04  -0.793  0.42810    
## stat88      -2.313e-04  2.454e-04  -0.942  0.34604    
## stat89      -3.285e-04  2.451e-04  -1.340  0.18027    
## stat90      -2.817e-04  2.483e-04  -1.134  0.25678    
## stat91      -4.300e-04  2.467e-04  -1.743  0.08140 .  
## stat92      -2.285e-04  2.480e-04  -0.921  0.35694    
## stat93      -9.587e-05  2.502e-04  -0.383  0.70155    
## stat94      -2.673e-05  2.466e-04  -0.108  0.91369    
## stat95      -1.052e-04  2.485e-04  -0.423  0.67213    
## stat96      -3.504e-04  2.460e-04  -1.425  0.15433    
## stat97      -2.797e-05  2.461e-04  -0.114  0.90954    
## stat98       3.531e-03  2.445e-04  14.442  < 2e-16 ***
## stat99       4.495e-05  2.489e-04   0.181  0.85667    
## stat100      4.922e-04  2.481e-04   1.984  0.04730 *  
## stat101     -7.072e-05  2.495e-04  -0.283  0.77685    
## stat102      1.614e-04  2.491e-04   0.648  0.51704    
## stat103     -7.755e-06  2.503e-04  -0.031  0.97529    
## stat104     -1.423e-04  2.476e-04  -0.575  0.56546    
## stat105      3.005e-04  2.452e-04   1.226  0.22037    
## stat106     -6.922e-05  2.468e-04  -0.280  0.77914    
## stat107     -4.644e-05  2.472e-04  -0.188  0.85099    
## stat108     -2.835e-04  2.473e-04  -1.147  0.25158    
## stat109     -2.545e-05  2.467e-04  -0.103  0.91785    
## stat110     -3.475e-03  2.483e-04 -13.995  < 2e-16 ***
## stat111      9.508e-06  2.466e-04   0.039  0.96925    
## stat112     -2.202e-05  2.501e-04  -0.088  0.92984    
## stat113     -1.389e-04  2.481e-04  -0.560  0.57572    
## stat114      4.755e-05  2.466e-04   0.193  0.84712    
## stat115      1.458e-04  2.473e-04   0.590  0.55546    
## stat116      2.875e-04  2.489e-04   1.155  0.24810    
## stat117      1.622e-04  2.500e-04   0.649  0.51664    
## stat118     -2.623e-04  2.457e-04  -1.068  0.28578    
## stat119      6.218e-05  2.479e-04   0.251  0.80200    
## stat120      8.084e-05  2.478e-04   0.326  0.74428    
## stat121     -2.385e-04  2.485e-04  -0.960  0.33708    
## stat122     -5.800e-06  2.456e-04  -0.024  0.98116    
## stat123     -2.556e-05  2.500e-04  -0.102  0.91857    
## stat124     -7.468e-06  2.485e-04  -0.030  0.97603    
## stat125      1.178e-04  2.485e-04   0.474  0.63555    
## stat126      1.513e-04  2.465e-04   0.614  0.53925    
## stat127      2.473e-04  2.461e-04   1.005  0.31487    
## stat128     -1.034e-04  2.474e-04  -0.418  0.67610    
## stat129      5.386e-05  2.457e-04   0.219  0.82651    
## stat130      4.596e-04  2.462e-04   1.867  0.06192 .  
## stat131     -9.985e-06  2.482e-04  -0.040  0.96791    
## stat132     -5.464e-05  2.456e-04  -0.223  0.82391    
## stat133      6.713e-05  2.469e-04   0.272  0.78570    
## stat134     -2.619e-04  2.460e-04  -1.065  0.28703    
## stat135     -6.020e-06  2.482e-04  -0.024  0.98065    
## stat136     -2.823e-04  2.496e-04  -1.131  0.25806    
## stat137      5.450e-05  2.453e-04   0.222  0.82417    
## stat138      3.746e-05  2.467e-04   0.152  0.87932    
## stat139      1.098e-04  2.489e-04   0.441  0.65915    
## stat140      9.217e-05  2.462e-04   0.374  0.70816    
## stat141      2.671e-04  2.464e-04   1.084  0.27851    
## stat142     -1.296e-04  2.497e-04  -0.519  0.60371    
## stat143      3.722e-05  2.476e-04   0.150  0.88053    
## stat144      5.702e-04  2.462e-04   2.316  0.02057 *  
## stat145     -6.333e-05  2.509e-04  -0.252  0.80077    
## stat146     -5.783e-04  2.479e-04  -2.332  0.01971 *  
## stat147     -3.060e-04  2.489e-04  -1.229  0.21897    
## stat148     -3.749e-04  2.457e-04  -1.526  0.12713    
## stat149     -4.942e-04  2.489e-04  -1.986  0.04711 *  
## stat150      6.109e-05  2.487e-04   0.246  0.80598    
## stat151     -3.107e-04  2.499e-04  -1.244  0.21367    
## stat152     -1.324e-04  2.480e-04  -0.534  0.59359    
## stat153      2.898e-05  2.508e-04   0.116  0.90800    
## stat154     -4.313e-06  2.491e-04  -0.017  0.98619    
## stat155      4.102e-05  2.466e-04   0.166  0.86786    
## stat156      4.230e-04  2.494e-04   1.696  0.08998 .  
## stat157     -1.637e-05  2.467e-04  -0.066  0.94709    
## stat158     -3.325e-04  2.511e-04  -1.324  0.18548    
## stat159      1.243e-04  2.460e-04   0.505  0.61331    
## stat160      1.515e-04  2.491e-04   0.608  0.54309    
## stat161      1.421e-04  2.484e-04   0.572  0.56724    
## stat162      1.916e-04  2.448e-04   0.783  0.43388    
## stat163      1.102e-04  2.499e-04   0.441  0.65927    
## stat164      6.529e-05  2.499e-04   0.261  0.79392    
## stat165      6.332e-05  2.461e-04   0.257  0.79698    
## stat166     -3.184e-04  2.448e-04  -1.301  0.19340    
## stat167     -1.192e-04  2.467e-04  -0.483  0.62888    
## stat168      1.678e-06  2.470e-04   0.007  0.99458    
## stat169     -8.484e-05  2.484e-04  -0.342  0.73269    
## stat170     -6.142e-06  2.472e-04  -0.025  0.98018    
## stat171      4.180e-07  2.512e-04   0.002  0.99867    
## stat172      2.706e-04  2.460e-04   1.100  0.27145    
## stat173     -1.686e-04  2.494e-04  -0.676  0.49893    
## stat174     -8.917e-05  2.478e-04  -0.360  0.71900    
## stat175     -5.480e-04  2.485e-04  -2.205  0.02750 *  
## stat176      1.059e-04  2.480e-04   0.427  0.66930    
## stat177     -1.307e-04  2.481e-04  -0.527  0.59848    
## stat178     -1.303e-05  2.501e-04  -0.052  0.95845    
## stat179      2.615e-04  2.480e-04   1.054  0.29179    
## stat180     -5.409e-04  2.460e-04  -2.199  0.02791 *  
## stat181      2.874e-04  2.481e-04   1.158  0.24674    
## stat182     -7.420e-05  2.488e-04  -0.298  0.76557    
## stat183     -1.106e-04  2.475e-04  -0.447  0.65501    
## stat184      5.259e-05  2.484e-04   0.212  0.83235    
## stat185     -2.140e-04  2.443e-04  -0.876  0.38107    
## stat186     -1.500e-04  2.488e-04  -0.603  0.54672    
## stat187     -2.712e-04  2.474e-04  -1.096  0.27302    
## stat188     -2.179e-04  2.475e-04  -0.880  0.37868    
## stat189      5.510e-05  2.474e-04   0.223  0.82378    
## stat190     -1.139e-04  2.480e-04  -0.459  0.64602    
## stat191     -3.396e-04  2.485e-04  -1.367  0.17180    
## stat192      1.112e-04  2.496e-04   0.446  0.65586    
## stat193     -2.441e-04  2.499e-04  -0.977  0.32868    
## stat194      2.095e-04  2.469e-04   0.848  0.39622    
## stat195      3.117e-04  2.465e-04   1.265  0.20599    
## stat196     -6.684e-05  2.509e-04  -0.266  0.78994    
## stat197      2.593e-04  2.454e-04   1.057  0.29071    
## stat198     -3.316e-04  2.485e-04  -1.335  0.18202    
## stat199      1.953e-04  2.461e-04   0.794  0.42748    
## stat200     -2.023e-04  2.435e-04  -0.831  0.40612    
## stat201     -8.103e-05  2.473e-04  -0.328  0.74322    
## stat202     -3.188e-04  2.524e-04  -1.263  0.20665    
## stat203      1.211e-04  2.467e-04   0.491  0.62341    
## stat204     -5.996e-04  2.458e-04  -2.439  0.01476 *  
## stat205     -2.209e-04  2.468e-04  -0.895  0.37079    
## stat206     -1.432e-04  2.505e-04  -0.572  0.56751    
## stat207      4.225e-04  2.479e-04   1.704  0.08844 .  
## stat208      1.188e-04  2.468e-04   0.481  0.63036    
## stat209     -1.294e-04  2.468e-04  -0.524  0.60004    
## stat210     -7.913e-05  2.483e-04  -0.319  0.74997    
## stat211     -4.470e-05  2.489e-04  -0.180  0.85752    
## stat212      2.229e-05  2.475e-04   0.090  0.92824    
## stat213     -3.187e-04  2.496e-04  -1.277  0.20165    
## stat214     -3.946e-04  2.472e-04  -1.597  0.11041    
## stat215     -2.788e-04  2.474e-04  -1.127  0.25983    
## stat216     -1.133e-04  2.481e-04  -0.457  0.64779    
## stat217      2.681e-04  2.483e-04   1.080  0.28037    
## x18.sqrt     2.587e-02  9.422e-04  27.461  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.03136 on 5343 degrees of freedom
## Multiple R-squared:  0.2678, Adjusted R-squared:  0.235 
## F-statistic: 8.144 on 240 and 5343 DF,  p-value: < 2.2e-16

cd.full = plot.diagnostics(model=model.full, train=data.train)

## [1] "Number of data points that have Cook's D > 4/n: 292"
>>>>>>> 8e6f61bca4894b586983e20a3e14b1b8a049b903
## [1] "Number of data points that have Cook's D > 1: 0"

Checking with removal of high influence points

high.cd = names(cd.full[cd.full > 4/nrow(data.train)])

#save dataset with high.cd flagged
t = data.train %>% 
  rownames_to_column() %>%
  mutate(high.cd = ifelse(rowname %in% high.cd,1,0))
#write.csv(t,file='data_high_cd_flag.csv',row.names = F)
###
data.train2 = data.train[!(rownames(data.train)) %in% high.cd,]
model.full2 = lm(formula , data.train2)
summary(model.full2)

## 
## Call:
## lm(formula = formula, data = data.train2)
## 
## Residuals:
##       Min        1Q    Median        3Q       Max 
## -0.057402 -0.017407 -0.002489  0.016456  0.069740 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  1.958e+00  7.793e-03 251.224  < 2e-16 ***
## x1          -4.485e-04  5.344e-04  -0.839 0.401415    
## x2           4.589e-04  3.391e-04   1.354 0.175951    
## x3          -3.649e-05  9.361e-05  -0.390 0.696695    
## x4          -4.964e-05  7.376e-06  -6.730 1.89e-11 ***
## x5           3.681e-04  2.404e-04   1.531 0.125876    
## x6          -4.350e-04  4.841e-04  -0.899 0.368928    
## x7           1.162e-02  5.212e-04  22.298  < 2e-16 ***
## x8           5.058e-04  1.216e-04   4.159 3.26e-05 ***
## x9           3.042e-03  2.697e-04  11.277  < 2e-16 ***
## x10          1.697e-03  2.522e-04   6.728 1.92e-11 ***
## x11          2.168e+05  6.030e+04   3.595 0.000327 ***
## x12          2.833e-04  1.534e-04   1.848 0.064727 .  
## x13          1.437e-04  6.122e-05   2.347 0.018940 *  
## x14         -1.507e-04  2.645e-04  -0.570 0.568935    
## x15          4.930e-05  2.509e-04   0.197 0.844209    
## x16          1.021e-03  1.746e-04   5.849 5.26e-09 ***
## x17          1.888e-03  2.657e-04   7.106 1.36e-12 ***
## x19          3.021e-05  1.348e-04   0.224 0.822685    
## x20         -7.862e-04  9.437e-04  -0.833 0.404837    
## x21          1.084e-04  3.448e-05   3.143 0.001681 ** 
## x22         -5.405e-04  2.825e-04  -1.913 0.055802 .  
## x23          4.950e-04  2.690e-04   1.840 0.065838 .  
## stat1       -1.969e-04  2.024e-04  -0.973 0.330548    
## stat2        1.577e-04  2.009e-04   0.785 0.432425    
## stat3        4.829e-04  2.026e-04   2.383 0.017193 *  
## stat4       -5.465e-04  2.041e-04  -2.678 0.007434 ** 
## stat5       -2.116e-04  2.028e-04  -1.043 0.296854    
## stat6       -1.450e-04  2.027e-04  -0.716 0.474318    
## stat7       -9.444e-05  2.020e-04  -0.468 0.640110    
## stat8        1.058e-04  2.021e-04   0.524 0.600633    
## stat9       -3.038e-04  2.021e-04  -1.503 0.132819    
## stat10      -1.673e-04  2.024e-04  -0.827 0.408333    
## stat11      -1.519e-04  2.036e-04  -0.746 0.455811    
## stat12       2.748e-04  2.017e-04   1.363 0.173082    
## stat13      -6.344e-04  2.010e-04  -3.156 0.001608 ** 
## stat14      -9.291e-04  2.009e-04  -4.624 3.85e-06 ***
## stat15      -4.833e-04  2.007e-04  -2.408 0.016094 *  
## stat16      -3.055e-05  2.015e-04  -0.152 0.879510    
## stat17       5.819e-05  2.009e-04   0.290 0.772084    
## stat18      -3.256e-04  2.021e-04  -1.611 0.107298    
## stat19      -5.567e-05  2.020e-04  -0.276 0.782908    
## stat20       3.081e-04  2.031e-04   1.517 0.129430    
## stat21       7.033e-05  2.028e-04   0.347 0.728740    
## stat22      -1.803e-04  2.032e-04  -0.887 0.374943    
## stat23       5.277e-04  2.023e-04   2.609 0.009108 ** 
## stat24      -4.754e-04  2.033e-04  -2.339 0.019380 *  
## stat25      -4.074e-04  2.016e-04  -2.021 0.043330 *  
## stat26      -4.563e-04  2.021e-04  -2.258 0.023987 *  
## stat27       2.053e-05  2.033e-04   0.101 0.919565    
## stat28      -9.001e-07  2.027e-04  -0.004 0.996457    
## stat29       1.711e-04  2.038e-04   0.840 0.401068    
## stat30       9.739e-05  2.029e-04   0.480 0.631216    
## stat31       1.248e-04  2.036e-04   0.613 0.539965    
## stat32       2.258e-04  2.032e-04   1.111 0.266524    
## stat33      -4.061e-04  2.023e-04  -2.007 0.044782 *  
## stat34       2.009e-04  2.019e-04   0.995 0.319766    
## stat35      -5.055e-04  2.020e-04  -2.502 0.012365 *  
## stat36      -1.727e-04  2.009e-04  -0.860 0.389954    
## stat37      -7.459e-05  2.042e-04  -0.365 0.714877    
## stat38       5.699e-04  2.012e-04   2.832 0.004647 ** 
## stat39      -2.856e-04  1.998e-04  -1.429 0.152967    
## stat40      -6.039e-05  2.026e-04  -0.298 0.765707    
## stat41      -6.258e-04  2.005e-04  -3.121 0.001814 ** 
## stat42      -1.348e-04  2.012e-04  -0.670 0.502989    
## stat43      -1.203e-04  2.032e-04  -0.592 0.553689    
## stat44      -2.554e-07  2.026e-04  -0.001 0.998994    
## stat45      -2.444e-04  2.024e-04  -1.207 0.227357    
## stat46       4.196e-05  2.024e-04   0.207 0.835776    
## stat47       4.968e-05  2.044e-04   0.243 0.807946    
## stat48       3.212e-04  2.022e-04   1.589 0.112155    
## stat49      -2.172e-05  2.019e-04  -0.108 0.914355    
## stat50       1.866e-04  1.999e-04   0.934 0.350530    
## stat51       1.251e-04  2.021e-04   0.619 0.535916    
## stat52       2.149e-04  2.027e-04   1.060 0.288992    
## stat53      -1.514e-04  2.042e-04  -0.742 0.458257    
## stat54      -2.520e-04  2.037e-04  -1.237 0.216170    
## stat55       9.376e-05  2.006e-04   0.467 0.640165    
## stat56       1.495e-04  2.026e-04   0.738 0.460753    
## stat57      -2.171e-04  2.006e-04  -1.082 0.279390    
## stat58      -4.828e-05  2.014e-04  -0.240 0.810583    
## stat59       1.827e-04  2.018e-04   0.905 0.365417    
## stat60       4.344e-04  2.024e-04   2.146 0.031926 *  
## stat61      -5.697e-05  2.028e-04  -0.281 0.778801    
## stat62      -3.749e-04  2.016e-04  -1.859 0.063040 .  
## stat63      -1.158e-04  2.022e-04  -0.573 0.566924    
## stat64       1.159e-06  2.011e-04   0.006 0.995403    
## stat65      -4.208e-04  2.045e-04  -2.058 0.039685 *  
## stat66      -3.552e-05  2.044e-04  -0.174 0.862029    
## stat67       3.680e-04  2.035e-04   1.809 0.070558 .  
## stat68      -2.074e-04  2.032e-04  -1.021 0.307309    
## stat69      -1.860e-04  2.031e-04  -0.916 0.359812    
## stat70       3.842e-04  2.011e-04   1.910 0.056199 .  
## stat71       1.170e-04  2.015e-04   0.581 0.561453    
## stat72       2.540e-05  2.031e-04   0.125 0.900490    
## stat73       3.495e-04  2.037e-04   1.716 0.086233 .  
## stat74       2.305e-04  2.030e-04   1.135 0.256427    
## stat75      -9.731e-06  2.044e-04  -0.048 0.962032    
## stat76       5.054e-05  2.031e-04   0.249 0.803475    
## stat77      -1.055e-04  2.022e-04  -0.522 0.601826    
## stat78      -3.665e-04  2.012e-04  -1.821 0.068629 .  
## stat79      -1.757e-05  2.011e-04  -0.087 0.930358    
## stat80       2.436e-04  2.024e-04   1.204 0.228752    
## stat81       1.247e-04  2.030e-04   0.614 0.539058    
## stat82      -2.036e-05  2.024e-04  -0.101 0.919862    
## stat83       1.422e-04  2.020e-04   0.704 0.481610    
## stat84      -1.581e-04  2.023e-04  -0.782 0.434413    
## stat85      -2.017e-04  2.018e-04  -0.999 0.317666    
## stat86       5.429e-04  2.023e-04   2.684 0.007301 ** 
## stat87      -2.278e-04  2.033e-04  -1.121 0.262388    
## stat88      -6.315e-05  2.010e-04  -0.314 0.753354    
## stat89      -4.190e-05  2.007e-04  -0.209 0.834618    
## stat90      -4.168e-04  2.029e-04  -2.055 0.039970 *  
## stat91      -4.513e-04  2.010e-04  -2.245 0.024804 *  
## stat92       9.969e-06  2.023e-04   0.049 0.960701    
## stat93       1.250e-05  2.047e-04   0.061 0.951289    
## stat94       2.366e-04  2.009e-04   1.178 0.238958    
## stat95       1.654e-04  2.034e-04   0.813 0.416096    
## stat96      -2.403e-04  2.012e-04  -1.195 0.232322    
## stat97       3.326e-05  2.011e-04   0.165 0.868651    
## stat98       3.394e-03  1.997e-04  16.990  < 2e-16 ***
## stat99       1.566e-04  2.034e-04   0.770 0.441340    
## stat100      5.538e-04  2.026e-04   2.733 0.006302 ** 
## stat101     -3.316e-05  2.044e-04  -0.162 0.871154    
## stat102      1.675e-04  2.034e-04   0.824 0.410127    
## stat103     -5.062e-05  2.040e-04  -0.248 0.804071    
## stat104     -1.259e-05  2.030e-04  -0.062 0.950571    
## stat105      3.880e-04  2.005e-04   1.935 0.053013 .  
## stat106     -8.101e-05  2.013e-04  -0.402 0.687381    
## stat107     -1.209e-04  2.021e-04  -0.598 0.549576    
## stat108     -1.702e-04  2.020e-04  -0.843 0.399474    
## stat109     -1.844e-04  2.014e-04  -0.916 0.359922    
## stat110     -3.418e-03  2.025e-04 -16.881  < 2e-16 ***
## stat111      3.945e-05  2.010e-04   0.196 0.844417    
## stat112     -6.677e-05  2.049e-04  -0.326 0.744554    
## stat113     -8.058e-05  2.025e-04  -0.398 0.690665    
## stat114      2.428e-04  2.018e-04   1.203 0.228979    
## stat115      2.145e-04  2.025e-04   1.059 0.289495    
## stat116      3.678e-04  2.036e-04   1.806 0.070903 .  
## stat117      1.865e-04  2.037e-04   0.915 0.360023    
## stat118     -1.061e-05  2.009e-04  -0.053 0.957861    
## stat119      2.434e-04  2.024e-04   1.202 0.229264    
## stat120     -3.393e-05  2.025e-04  -0.168 0.866951    
## stat121     -1.850e-04  2.032e-04  -0.911 0.362589    
## stat122     -9.087e-05  2.011e-04  -0.452 0.651335    
## stat123      1.432e-04  2.037e-04   0.703 0.482178    
## stat124     -2.001e-04  2.032e-04  -0.985 0.324758    
## stat125     -4.645e-05  2.032e-04  -0.229 0.819212    
## stat126      2.135e-04  2.016e-04   1.059 0.289809    
## stat127      8.548e-05  2.006e-04   0.426 0.670073    
## stat128     -3.362e-04  2.016e-04  -1.667 0.095558 .  
## stat129      5.658e-05  2.007e-04   0.282 0.778061    
## stat130      2.695e-04  2.011e-04   1.340 0.180210    
## stat131      3.673e-05  2.020e-04   0.182 0.855707    
## stat132     -1.013e-04  2.009e-04  -0.504 0.614039    
## stat133      4.747e-05  2.021e-04   0.235 0.814332    
## stat134     -1.031e-04  2.007e-04  -0.514 0.607371    
## stat135     -9.950e-05  2.030e-04  -0.490 0.624098    
## stat136     -4.771e-04  2.035e-04  -2.344 0.019097 *  
## stat137      1.371e-04  2.000e-04   0.685 0.493226    
## stat138     -1.019e-04  2.013e-04  -0.506 0.612851    
## stat139     -5.271e-05  2.035e-04  -0.259 0.795626    
## stat140      2.777e-04  2.005e-04   1.385 0.166130    
## stat141      4.438e-04  2.012e-04   2.206 0.027411 *  
## stat142      9.528e-05  2.040e-04   0.467 0.640452    
## stat143     -1.636e-05  2.028e-04  -0.081 0.935711    
## stat144      4.676e-04  2.011e-04   2.325 0.020090 *  
## stat145     -6.764e-06  2.051e-04  -0.033 0.973692    
## stat146     -7.726e-04  2.024e-04  -3.816 0.000137 ***
## stat147     -2.043e-04  2.039e-04  -1.002 0.316423    
## stat148     -2.628e-04  2.014e-04  -1.305 0.191996    
## stat149     -4.906e-04  2.034e-04  -2.412 0.015881 *  
## stat150     -2.339e-05  2.033e-04  -0.115 0.908411    
## stat151      2.439e-05  2.047e-04   0.119 0.905171    
## stat152     -9.612e-05  2.022e-04  -0.475 0.634569    
## stat153      3.326e-04  2.047e-04   1.625 0.104314    
## stat154      2.337e-05  2.037e-04   0.115 0.908648    
## stat155      2.869e-04  2.016e-04   1.423 0.154790    
## stat156      3.253e-04  2.037e-04   1.597 0.110313    
## stat157      1.091e-04  2.015e-04   0.542 0.588171    
## stat158      2.764e-05  2.051e-04   0.135 0.892782    
## stat159      2.493e-04  2.007e-04   1.242 0.214385    
## stat160      4.662e-05  2.040e-04   0.229 0.819223    
## stat161     -5.186e-05  2.028e-04  -0.256 0.798158    
## stat162      1.695e-04  1.998e-04   0.848 0.396326    
## stat163      1.241e-04  2.049e-04   0.606 0.544809    
## stat164     -1.805e-04  2.044e-04  -0.883 0.377147    
## stat165      8.224e-05  2.014e-04   0.408 0.683043    
## stat166     -2.284e-04  1.997e-04  -1.144 0.252631    
## stat167     -1.492e-04  2.016e-04  -0.740 0.459319    
## stat168     -3.093e-05  2.011e-04  -0.154 0.877762    
## stat169     -2.426e-04  2.033e-04  -1.193 0.232902    
## stat170      6.964e-05  2.015e-04   0.346 0.729656    
## stat171     -8.456e-05  2.050e-04  -0.413 0.679972    
## stat172      5.647e-04  2.005e-04   2.817 0.004868 ** 
## stat173     -3.167e-05  2.036e-04  -0.156 0.876411    
## stat174      3.106e-06  2.026e-04   0.015 0.987772    
## stat175     -4.993e-04  2.028e-04  -2.462 0.013844 *  
## stat176     -1.971e-04  2.027e-04  -0.972 0.330934    
## stat177     -4.236e-04  2.025e-04  -2.091 0.036536 *  
## stat178     -3.418e-05  2.043e-04  -0.167 0.867136    
## stat179      2.119e-04  2.024e-04   1.047 0.295155    
## stat180     -4.758e-04  2.016e-04  -2.361 0.018285 *  
## stat181      3.535e-04  2.025e-04   1.745 0.080966 .  
## stat182      1.388e-04  2.039e-04   0.681 0.496092    
## stat183      6.291e-05  2.023e-04   0.311 0.755798    
## stat184      3.568e-04  2.024e-04   1.763 0.077933 .  
## stat185     -3.456e-05  1.993e-04  -0.173 0.862363    
## stat186      1.472e-04  2.032e-04   0.725 0.468726    
## stat187     -2.581e-04  2.017e-04  -1.280 0.200651    
## stat188     -2.191e-05  2.022e-04  -0.108 0.913714    
## stat189     -2.893e-05  2.025e-04  -0.143 0.886360    
## stat190     -3.321e-04  2.030e-04  -1.636 0.101942    
## stat191     -4.327e-04  2.027e-04  -2.135 0.032820 *  
## stat192     -4.255e-06  2.041e-04  -0.021 0.983373    
## stat193     -1.323e-04  2.044e-04  -0.647 0.517416    
## stat194     -4.192e-05  2.020e-04  -0.207 0.835654    
## stat195      1.785e-04  2.014e-04   0.886 0.375539    
## stat196     -1.287e-04  2.049e-04  -0.628 0.530144    
## stat197      1.724e-05  2.007e-04   0.086 0.931560    
## stat198     -3.170e-04  2.029e-04  -1.562 0.118338    
## stat199      1.249e-04  2.010e-04   0.621 0.534479    
## stat200     -1.739e-04  1.993e-04  -0.873 0.382730    
## stat201      4.440e-06  2.026e-04   0.022 0.982520    
## stat202     -1.694e-04  2.061e-04  -0.822 0.411157    
## stat203      1.650e-04  2.016e-04   0.818 0.413145    
## stat204     -1.992e-04  2.012e-04  -0.990 0.322336    
## stat205      7.847e-05  2.011e-04   0.390 0.696387    
## stat206     -3.098e-04  2.046e-04  -1.514 0.130001    
## stat207      4.263e-04  2.028e-04   2.102 0.035603 *  
## stat208      2.016e-04  2.021e-04   0.998 0.318446    
## stat209     -5.689e-07  2.012e-04  -0.003 0.997744    
## stat210     -2.808e-04  2.029e-04  -1.384 0.166298    
## stat211     -4.572e-05  2.038e-04  -0.224 0.822500    
## stat212      1.117e-04  2.023e-04   0.552 0.580940    
## stat213     -2.776e-04  2.034e-04  -1.365 0.172341    
## stat214     -2.307e-04  2.018e-04  -1.143 0.252911    
## stat215     -1.129e-04  2.025e-04  -0.557 0.577312    
## stat216     -1.670e-04  2.023e-04  -0.826 0.409076    
## stat217      1.638e-04  2.026e-04   0.809 0.418726    
## x18.sqrt     2.558e-02  7.679e-04  33.311  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.02491 on 5051 degrees of freedom
## Multiple R-squared:  0.3734, Adjusted R-squared:  0.3437 
## F-statistic: 12.54 on 240 and 5051 DF,  p-value: < 2.2e-16

cd.full2 = plot.diagnostics(model.full2, data.train2)

## [1] "Number of data points that have Cook's D > 4/n: 265"
## [1] "Number of data points that have Cook's D > 1: 0"

# much more normal residuals than before. 
# Checking to see if distributions are different and if so whcih variables
# High Leverage Plot 
plotData = data.train %>% 
  rownames_to_column() %>%
  mutate(type=ifelse(rowname %in% high.cd,'High','Normal')) %>%
  dplyr::select(type,target=one_of(label.names))

ggplot(data=plotData, aes(x=type,y=target)) +
  geom_boxplot(fill='light blue',outlier.shape=NA) +
  scale_y_continuous(name="Target Variable Values",label=scales::comma_format(accuracy=.1)) +
  theme_light() +
  ggtitle('Distribution of High Leverage Points and Normal  Points')

# 2 sample t-tests

plotData = data.train %>% 
  rownames_to_column() %>%
  mutate(type=ifelse(rowname %in% high.cd,'High','Normal')) %>%
  dplyr::select(type,one_of(feature.names))

comp.test = lapply(dplyr::select(plotData, one_of(feature.names))
                   , function(x) t.test(x ~ plotData$type, var.equal = TRUE)) 

sig.comp = list.filter(comp.test, p.value < 0.05)
sapply(sig.comp, function(x) x[['p.value']])

<<<<<<< HEAD

##           x4          x14       stat22       stat67       stat74       stat82       stat85       stat95       stat98 
## 1.272018e-02 2.501255e-02 4.594164e-02 3.146324e-02 3.462500e-02 2.956704e-02 1.632652e-02 4.422400e-02 5.613321e-05 
##      stat110      stat128      stat146      stat155      stat186 
## 7.445871e-04 1.127701e-04 2.322952e-02 2.116008e-02 2.106983e-02

=======

##           x6        stat4       stat22       stat47       stat82       stat85       stat95       stat98      stat110 
## 4.711617e-02 6.946036e-03 4.924546e-02 1.995137e-02 1.000120e-02 2.362890e-02 4.571544e-02 2.161598e-06 3.971208e-04 
##      stat128      stat146      stat151      stat169      stat172      stat204     x18.sqrt 
## 9.211091e-03 6.623412e-03 1.023297e-02 1.972685e-02 3.262764e-02 2.931977e-02 3.083623e-02

>>>>>>> 8e6f61bca4894b586983e20a3e14b1b8a049b903

mm = melt(plotData, id=c('type')) %>% filter(variable %in% names(sig.comp))

ggplot(mm,aes(x=type, y=value)) +
  geom_boxplot()+
  facet_wrap(~variable, ncol=5, scales = 'free_y') +
  scale_y_continuous(name="values",label=scales::comma_format(accuracy=.1)) +
  ggtitle('Distribution of High Leverage Points and Normal Points')

<<<<<<< HEAD

=======

>>>>>>> 8e6f61bca4894b586983e20a3e14b1b8a049b903

# Distribution (box) Plots
mm = melt(plotData, id=c('type'))

ggplot(mm,aes(x=type, y=value)) +
  geom_boxplot()+
  facet_wrap(~variable, ncol=8, scales = 'free_y') +
  scale_y_continuous(name="values",label=scales::comma_format(accuracy=.1)) +
  ggtitle('Distribution of High Leverage Points and Normal Points')

Grand Means Model

model.null = lm(grand.mean.formula, data.train)
summary(model.null)

## 
## Call:
## lm(formula = grand.mean.formula, data = data.train)
## 
## Residuals:
##       Min        1Q    Median        3Q       Max 
<<<<<<< HEAD
## -0.115038 -0.023938 -0.003437  0.020538  0.190275 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 2.0969137  0.0004839    4333   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.03616 on 5583 degrees of freedom

======= ## -0.114839 -0.023677 -0.003183 0.020570 0.175063 ## ## Coefficients: ## Estimate Std. Error t value Pr(>|t|) ## (Intercept) 2.0967148 0.0004799 4369 <2e-16 *** ## --- ## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 ## ## Residual standard error: 0.03586 on 5583 degrees of freedom >>>>>>> 8e6f61bca4894b586983e20a3e14b1b8a049b903

Variable Selection

Basic: http://www.stat.columbia.edu/~martin/W2024/R10.pdf Cross Validation + Other Metrics: http://www.sthda.com/english/articles/37-model-selection-essentials-in-r/154-stepwise-regression-essentials-in-r/

Forward Selection with CV

Train

if (algo.forward.caret == TRUE){
  set.seed(1)
  returned = train.caret.glmselect(formula = formula
                                   , data = data.train
                                   , method = "leapForward"
                                   , feature.names = feature.names)
  model.forward = returned$model
  id = returned$id
}

## Aggregating results
## Selecting tuning parameters
<<<<<<< HEAD
## Fitting nvmax = 7 on full training set
## [1] "All models results"
##     nvmax       RMSE  Rsquared        MAE       RMSESD RsquaredSD        MAESD
## 1       1 0.03425332 0.1038025 0.02663970 0.0006637466 0.02345731 0.0004078960
## 2       2 0.03345274 0.1456791 0.02595410 0.0006744402 0.02299972 0.0005397020
## 3       3 0.03287356 0.1755708 0.02542164 0.0007428313 0.03453720 0.0006065015
## 4       4 0.03238568 0.2002338 0.02476762 0.0007588086 0.03652502 0.0005318967
## 5       5 0.03210370 0.2138463 0.02455180 0.0007501264 0.03860748 0.0004926778
## 6       6 0.03207281 0.2152005 0.02457183 0.0007522223 0.03774776 0.0004857396
## 7       7 0.03198024 0.2196041 0.02449315 0.0007733914 0.03745117 0.0004793219
## 8       8 0.03202042 0.2177381 0.02451834 0.0007986437 0.03807747 0.0004689433
## 9       9 0.03202975 0.2172467 0.02453799 0.0008229237 0.03807716 0.0004777837
## 10     10 0.03204470 0.2166573 0.02458335 0.0008692181 0.03928587 0.0004970027
## 11     11 0.03205450 0.2163469 0.02459478 0.0008900320 0.04095855 0.0005215186
## 12     12 0.03202978 0.2176650 0.02459328 0.0009083095 0.04241137 0.0005532378
## 13     13 0.03203789 0.2172484 0.02458580 0.0009255880 0.04316006 0.0005482828
## 14     14 0.03201746 0.2181256 0.02456640 0.0009074620 0.04320969 0.0005352318
## 15     15 0.03200221 0.2187415 0.02456541 0.0008875529 0.04192161 0.0005198344
## 16     16 0.03200929 0.2183536 0.02456633 0.0008841716 0.04062908 0.0005175875
## 17     17 0.03200941 0.2183028 0.02457658 0.0008754303 0.04056618 0.0005016424
## 18     18 0.03200735 0.2184496 0.02456975 0.0008681755 0.04123859 0.0005068268
## 19     19 0.03201551 0.2181085 0.02457413 0.0008570310 0.04119713 0.0005148643
## 20     20 0.03202603 0.2176078 0.02457884 0.0008480833 0.03917978 0.0005005236
## 21     21 0.03202632 0.2177041 0.02459583 0.0008693105 0.04074689 0.0005038274
## 22     22 0.03204354 0.2169746 0.02461131 0.0008564701 0.04124006 0.0004985774
## 23     23 0.03206535 0.2160674 0.02462354 0.0008844102 0.04161250 0.0005130282
## 24     24 0.03207994 0.2154113 0.02464695 0.0008772836 0.04207940 0.0005196965
## 25     25 0.03209704 0.2147090 0.02465619 0.0008773609 0.04228189 0.0005116772
## 26     26 0.03211100 0.2140913 0.02466218 0.0008659019 0.04225409 0.0005187658
## 27     27 0.03212285 0.2136133 0.02466584 0.0008827717 0.04270849 0.0005242503
## 28     28 0.03215456 0.2121861 0.02469439 0.0008725705 0.04224414 0.0005156718
## 29     29 0.03218762 0.2107482 0.02470955 0.0008787025 0.04248352 0.0005324064
## 30     30 0.03218762 0.2107042 0.02470595 0.0008650116 0.04107858 0.0005241851
## 31     31 0.03220642 0.2098019 0.02472348 0.0008464269 0.04015817 0.0005140751
## 32     32 0.03222899 0.2087787 0.02474004 0.0008297812 0.03929632 0.0004989500
## 33     33 0.03225221 0.2077077 0.02476354 0.0008412632 0.03917881 0.0005148373
## 34     34 0.03225396 0.2076823 0.02476104 0.0008400931 0.03914337 0.0005024854
## 35     35 0.03225068 0.2078406 0.02476025 0.0008281323 0.03920479 0.0005063259
## 36     36 0.03226815 0.2070115 0.02477967 0.0008216528 0.03891611 0.0004838645
## 37     37 0.03226428 0.2072522 0.02477139 0.0008323671 0.03936488 0.0005022177
## 38     38 0.03226734 0.2072163 0.02476483 0.0008578724 0.03926701 0.0005138741
## 39     39 0.03228366 0.2064904 0.02477378 0.0008559894 0.03898850 0.0004998477
## 40     40 0.03227727 0.2067550 0.02475892 0.0008470391 0.03845076 0.0005151089
## 41     41 0.03227475 0.2068510 0.02476785 0.0008320415 0.03850472 0.0005087222
## 42     42 0.03227794 0.2066541 0.02476377 0.0008265100 0.03795841 0.0004964451
## 43     43 0.03229750 0.2057985 0.02477069 0.0008207917 0.03771944 0.0004914882
## 44     44 0.03230157 0.2057027 0.02477333 0.0008188554 0.03759670 0.0004896224
## 45     45 0.03230461 0.2056555 0.02476923 0.0008094334 0.03737533 0.0004756162
## 46     46 0.03230912 0.2055744 0.02476657 0.0008284662 0.03819449 0.0004832617
## 47     47 0.03231195 0.2054554 0.02476226 0.0008261027 0.03801366 0.0004963263
## 48     48 0.03231987 0.2051875 0.02477140 0.0008416278 0.03820537 0.0005113370
## 49     49 0.03231393 0.2055364 0.02475981 0.0008402889 0.03778873 0.0005245987
## 50     50 0.03231931 0.2053657 0.02476205 0.0008294511 0.03754007 0.0005273374
## 51     51 0.03231760 0.2054704 0.02475627 0.0008215351 0.03726838 0.0005238694
## 52     52 0.03231577 0.2056270 0.02475740 0.0008311694 0.03793016 0.0005298481
## 53     53 0.03231391 0.2057282 0.02474924 0.0008346159 0.03816937 0.0005342212
## 54     54 0.03232302 0.2053976 0.02475217 0.0008530000 0.03846713 0.0005383056
## 55     55 0.03231759 0.2056344 0.02474141 0.0008600879 0.03845304 0.0005507192
## 56     56 0.03231438 0.2058017 0.02473980 0.0008603944 0.03828008 0.0005559409
## 57     57 0.03232896 0.2051983 0.02475823 0.0008682246 0.03916968 0.0005667832
## 58     58 0.03234246 0.2046616 0.02476647 0.0008781541 0.03945602 0.0005785650
## 59     59 0.03234400 0.2046528 0.02476576 0.0008928999 0.03980144 0.0005940435
## 60     60 0.03233157 0.2052024 0.02475111 0.0008843889 0.03964404 0.0005846254
## 61     61 0.03234112 0.2048464 0.02476157 0.0008801030 0.03977207 0.0005808083
## 62     62 0.03234582 0.2047093 0.02477684 0.0008849383 0.03987738 0.0005884327
## 63     63 0.03233759 0.2050896 0.02477178 0.0008901416 0.04016549 0.0006084873
## 64     64 0.03234720 0.2046886 0.02477744 0.0008939146 0.04051177 0.0006085268
## 65     65 0.03234535 0.2047567 0.02478268 0.0008951426 0.04023932 0.0006137211
## 66     66 0.03235396 0.2043840 0.02479212 0.0008932029 0.03986344 0.0006145574
## 67     67 0.03234908 0.2046800 0.02478327 0.0009111084 0.04079861 0.0006304013
## 68     68 0.03234661 0.2047798 0.02478415 0.0009167986 0.04101754 0.0006319890
## 69     69 0.03234990 0.2046026 0.02478412 0.0009082548 0.04065113 0.0006179838
## 70     70 0.03234394 0.2048595 0.02478127 0.0008989999 0.04005898 0.0006191626
## 71     71 0.03234317 0.2049899 0.02477944 0.0009116507 0.04057801 0.0006319947
## 72     72 0.03234218 0.2050562 0.02477725 0.0009225632 0.04092472 0.0006289144
## 73     73 0.03234321 0.2050800 0.02477431 0.0009247104 0.04115610 0.0006401351
## 74     74 0.03234830 0.2048629 0.02477738 0.0009335101 0.04125402 0.0006462124
## 75     75 0.03234907 0.2047908 0.02477024 0.0009311665 0.04133942 0.0006425680
## 76     76 0.03234353 0.2050833 0.02475716 0.0009408045 0.04141778 0.0006444117
## 77     77 0.03235695 0.2045206 0.02476191 0.0009483779 0.04159505 0.0006463661
## 78     78 0.03235124 0.2047769 0.02475875 0.0009368024 0.04155216 0.0006278327
## 79     79 0.03233991 0.2052514 0.02474672 0.0009356728 0.04128415 0.0006253143
## 80     80 0.03233935 0.2052502 0.02474342 0.0009364226 0.04046615 0.0006293013
## 81     81 0.03235140 0.2047529 0.02474696 0.0009392787 0.04025579 0.0006282085
## 82     82 0.03234990 0.2048621 0.02474915 0.0009437216 0.04040662 0.0006406448
## 83     83 0.03235093 0.2048937 0.02474889 0.0009465195 0.04084632 0.0006503105
## 84     84 0.03235277 0.2048314 0.02475204 0.0009485554 0.04069506 0.0006572867
## 85     85 0.03235186 0.2048757 0.02475047 0.0009434288 0.04045353 0.0006524788
## 86     86 0.03235746 0.2046309 0.02475756 0.0009416367 0.04042292 0.0006549261
## 87     87 0.03236327 0.2043201 0.02476534 0.0009416268 0.04028398 0.0006608134
## 88     88 0.03237567 0.2038072 0.02478221 0.0009460851 0.04028672 0.0006616953
## 89     89 0.03237791 0.2037248 0.02478741 0.0009466909 0.04026254 0.0006586678
## 90     90 0.03238585 0.2033874 0.02479508 0.0009464895 0.04006450 0.0006524957
## 91     91 0.03238878 0.2032821 0.02480052 0.0009556147 0.04007944 0.0006638729
## 92     92 0.03238919 0.2032675 0.02480020 0.0009579794 0.03982103 0.0006570841
## 93     93 0.03239792 0.2029131 0.02480727 0.0009587934 0.04005396 0.0006601700
## 94     94 0.03241220 0.2022693 0.02481437 0.0009455669 0.03924290 0.0006530140
## 95     95 0.03241536 0.2020674 0.02482375 0.0009355865 0.03853373 0.0006376410
## 96     96 0.03242144 0.2017556 0.02483308 0.0009295837 0.03811159 0.0006375916
## 97     97 0.03243073 0.2013651 0.02484734 0.0009240696 0.03792972 0.0006410813
## 98     98 0.03242584 0.2016171 0.02484847 0.0009239515 0.03811274 0.0006413954
## 99     99 0.03242475 0.2016583 0.02485208 0.0009269770 0.03810114 0.0006484059
## 100   100 0.03242597 0.2015645 0.02485265 0.0009258770 0.03789101 0.0006452211
## 101   101 0.03242645 0.2015480 0.02485978 0.0009285266 0.03793818 0.0006485322
## 102   102 0.03242781 0.2014810 0.02486084 0.0009218449 0.03774888 0.0006443989
## 103   103 0.03242466 0.2016116 0.02485947 0.0009226232 0.03754371 0.0006416607
## 104   104 0.03242321 0.2016842 0.02485329 0.0009254970 0.03725555 0.0006363103
## 105   105 0.03243106 0.2013468 0.02485658 0.0009270190 0.03742344 0.0006426924
## 106   106 0.03242832 0.2015017 0.02485248 0.0009219362 0.03753943 0.0006345397
## 107   107 0.03243376 0.2013307 0.02485344 0.0009225388 0.03782821 0.0006398205
## 108   108 0.03243638 0.2012358 0.02485895 0.0009203937 0.03774353 0.0006338635
## 109   109 0.03243530 0.2013067 0.02485823 0.0009262451 0.03799016 0.0006355999
## 110   110 0.03243352 0.2013729 0.02485929 0.0009232081 0.03777778 0.0006267942
## 111   111 0.03244225 0.2009967 0.02486622 0.0009208366 0.03734784 0.0006276097
## 112   112 0.03244543 0.2008877 0.02486814 0.0009240197 0.03753100 0.0006271282
## 113   113 0.03243398 0.2013656 0.02486111 0.0009205469 0.03729800 0.0006193721
## 114   114 0.03243300 0.2014043 0.02485969 0.0009231327 0.03727070 0.0006196617
## 115   115 0.03244053 0.2010777 0.02486385 0.0009160425 0.03711190 0.0006095460
## 116   116 0.03244156 0.2010298 0.02486710 0.0009164051 0.03697066 0.0006065728
## 117   117 0.03243880 0.2011363 0.02487113 0.0009138376 0.03685727 0.0006070892
## 118   118 0.03243880 0.2011905 0.02487369 0.0009178758 0.03700262 0.0006196934
## 119   119 0.03244007 0.2011457 0.02487416 0.0009141491 0.03685142 0.0006225413
## 120   120 0.03243249 0.2014528 0.02487547 0.0009035198 0.03654021 0.0006124608
## 121   121 0.03243858 0.2012635 0.02488380 0.0009086119 0.03668680 0.0006170326
## 122   122 0.03243512 0.2014345 0.02488043 0.0009064722 0.03656364 0.0006117069
## 123   123 0.03243587 0.2013802 0.02487860 0.0009058547 0.03638222 0.0006088540
## 124   124 0.03243583 0.2014097 0.02488153 0.0009010734 0.03623152 0.0006107263
## 125   125 0.03243313 0.2015543 0.02487929 0.0009049914 0.03649795 0.0006085321
## 126   126 0.03243163 0.2016280 0.02488041 0.0009065971 0.03659907 0.0006102515
## 127   127 0.03243668 0.2014286 0.02488789 0.0009045333 0.03639173 0.0006050556
## 128   128 0.03243092 0.2016512 0.02488153 0.0009028268 0.03618705 0.0006036632
## 129   129 0.03243757 0.2013461 0.02488368 0.0009002642 0.03601815 0.0005985909
## 130   130 0.03243637 0.2013482 0.02488584 0.0008960741 0.03578918 0.0005920354
## 131   131 0.03243833 0.2012623 0.02488550 0.0008963951 0.03570313 0.0005951867
## 132   132 0.03244517 0.2009284 0.02489332 0.0008901719 0.03533913 0.0005906992
## 133   133 0.03244870 0.2007981 0.02489772 0.0008902826 0.03516049 0.0005834044
## 134   134 0.03245370 0.2005783 0.02489999 0.0008963292 0.03504266 0.0005901542
## 135   135 0.03245767 0.2004205 0.02490864 0.0008970495 0.03515772 0.0005985022
## 136   136 0.03247089 0.1998588 0.02492264 0.0008997920 0.03520020 0.0006001149
## 137   137 0.03247872 0.1995291 0.02492926 0.0009026981 0.03537158 0.0005986826
## 138   138 0.03247557 0.1996855 0.02492268 0.0008993834 0.03537595 0.0005953179
## 139   139 0.03247701 0.1996537 0.02492970 0.0008999057 0.03567589 0.0006017647
## 140   140 0.03248245 0.1994570 0.02493004 0.0008955063 0.03582755 0.0005989570
## 141   141 0.03247939 0.1996032 0.02492411 0.0008980332 0.03565632 0.0006035756
## 142   142 0.03248172 0.1995321 0.02492472 0.0008976698 0.03570799 0.0005974015
## 143   143 0.03248314 0.1994743 0.02492633 0.0008966188 0.03565448 0.0005953337
## 144   144 0.03248984 0.1991671 0.02493386 0.0008900063 0.03552741 0.0005917431
## 145   145 0.03249422 0.1990028 0.02493739 0.0008911373 0.03563544 0.0005885409
## 146   146 0.03249049 0.1991740 0.02493373 0.0008921655 0.03557022 0.0005936148
## 147   147 0.03248872 0.1992403 0.02493470 0.0008909599 0.03550745 0.0005947929
## 148   148 0.03249173 0.1990908 0.02493564 0.0008874795 0.03537123 0.0005906702
## 149   149 0.03248418 0.1994458 0.02492668 0.0008885112 0.03555083 0.0005933954
## 150   150 0.03248640 0.1993665 0.02492529 0.0008928167 0.03570149 0.0005955367
## 151   151 0.03248489 0.1994358 0.02492698 0.0008878432 0.03552644 0.0005925543
## 152   152 0.03248049 0.1996195 0.02492333 0.0008856623 0.03536552 0.0005901828
## 153   153 0.03247503 0.1998757 0.02491768 0.0008855359 0.03556416 0.0005870722
## 154   154 0.03247069 0.2000737 0.02491646 0.0008849520 0.03566817 0.0005848079
## 155   155 0.03247046 0.2000911 0.02491222 0.0008776927 0.03557668 0.0005777091
## 156   156 0.03247176 0.2000522 0.02491193 0.0008778872 0.03560527 0.0005828458
## 157   157 0.03247203 0.2000206 0.02490786 0.0008800305 0.03541244 0.0005833027
## 158   158 0.03247718 0.1997660 0.02490960 0.0008772766 0.03509925 0.0005819353
## 159   159 0.03247867 0.1997085 0.02490844 0.0008815291 0.03503918 0.0005860433
## 160   160 0.03248293 0.1995280 0.02491104 0.0008814234 0.03493910 0.0005853529
## 161   161 0.03248281 0.1995462 0.02491118 0.0008793696 0.03479915 0.0005799937
## 162   162 0.03248364 0.1995048 0.02491114 0.0008744203 0.03465827 0.0005792231
## 163   163 0.03248621 0.1994077 0.02491516 0.0008739026 0.03462654 0.0005826598
## 164   164 0.03248719 0.1993687 0.02491684 0.0008751988 0.03447777 0.0005808543
## 165   165 0.03248961 0.1992467 0.02492059 0.0008737361 0.03436242 0.0005782947
## 166   166 0.03248975 0.1992464 0.02492211 0.0008738415 0.03449333 0.0005731866
## 167   167 0.03248746 0.1993610 0.02491951 0.0008738797 0.03462349 0.0005751304
## 168   168 0.03248810 0.1993495 0.02491969 0.0008847457 0.03497328 0.0005832000
## 169   169 0.03249007 0.1992913 0.02491946 0.0008833885 0.03502697 0.0005822244
## 170   170 0.03248963 0.1993095 0.02491798 0.0008847103 0.03507500 0.0005854299
## 171   171 0.03248493 0.1995119 0.02491398 0.0008835991 0.03504001 0.0005862350
## 172   172 0.03248464 0.1995279 0.02491215 0.0008804676 0.03495792 0.0005849363
## 173   173 0.03248417 0.1995409 0.02491196 0.0008764807 0.03481496 0.0005801069
## 174   174 0.03248538 0.1994929 0.02491369 0.0008743601 0.03475987 0.0005799823
## 175   175 0.03248319 0.1995850 0.02491114 0.0008750088 0.03476820 0.0005796773
## 176   176 0.03248338 0.1996087 0.02491118 0.0008730968 0.03493957 0.0005772947
## 177   177 0.03248246 0.1996394 0.02491046 0.0008707840 0.03484665 0.0005784407
## 178   178 0.03248466 0.1995477 0.02491277 0.0008705731 0.03479142 0.0005803902
## 179   179 0.03248741 0.1994256 0.02491312 0.0008704373 0.03466812 0.0005782668
## 180   180 0.03248611 0.1994708 0.02491388 0.0008693338 0.03480152 0.0005798784
## 181   181 0.03248536 0.1994901 0.02491387 0.0008697065 0.03465894 0.0005776697
## 182   182 0.03248267 0.1996061 0.02491199 0.0008683756 0.03455420 0.0005750150
## 183   183 0.03248412 0.1995416 0.02491447 0.0008700606 0.03462214 0.0005780112
## 184   184 0.03248361 0.1995765 0.02491433 0.0008734609 0.03466139 0.0005789079
## 185   185 0.03248646 0.1994422 0.02491713 0.0008753482 0.03451757 0.0005765737
## 186   186 0.03248448 0.1995271 0.02491464 0.0008747700 0.03450348 0.0005784177
## 187   187 0.03248309 0.1995821 0.02491304 0.0008750297 0.03448864 0.0005776661
## 188   188 0.03248527 0.1994988 0.02491386 0.0008785071 0.03462768 0.0005825981
## 189   189 0.03248500 0.1994964 0.02491444 0.0008810888 0.03462785 0.0005837340
## 190   190 0.03248349 0.1995651 0.02491263 0.0008812024 0.03465382 0.0005826084
## 191   191 0.03248518 0.1995021 0.02491375 0.0008807648 0.03467276 0.0005838545
## 192   192 0.03248612 0.1994681 0.02491460 0.0008796605 0.03469117 0.0005832579
## 193   193 0.03248668 0.1994614 0.02491517 0.0008797943 0.03485550 0.0005869625
## 194   194 0.03249018 0.1993214 0.02491512 0.0008808198 0.03495191 0.0005894243
## 195   195 0.03248991 0.1993525 0.02491502 0.0008801786 0.03502950 0.0005905530
## 196   196 0.03249411 0.1991847 0.02491980 0.0008784703 0.03503171 0.0005888367
## 197   197 0.03249717 0.1990595 0.02492232 0.0008766760 0.03488136 0.0005876382
## 198   198 0.03249700 0.1990701 0.02492205 0.0008757393 0.03486623 0.0005874632
## 199   199 0.03249606 0.1991095 0.02492113 0.0008768510 0.03483606 0.0005869788
## 200   200 0.03249804 0.1990300 0.02492282 0.0008790443 0.03494330 0.0005911075
## 201   201 0.03249918 0.1989736 0.02492359 0.0008772378 0.03478190 0.0005879876
## 202   202 0.03249925 0.1989797 0.02492386 0.0008773952 0.03476409 0.0005909456
## 203   203 0.03249868 0.1990042 0.02492344 0.0008746218 0.03467848 0.0005862002
## 204   204 0.03249710 0.1990668 0.02492457 0.0008767562 0.03466324 0.0005860671
## 205   205 0.03249818 0.1990258 0.02492668 0.0008780947 0.03469432 0.0005871516
## 206   206 0.03249791 0.1990267 0.02492721 0.0008773839 0.03471409 0.0005887559
## 207   207 0.03249862 0.1990058 0.02492790 0.0008775362 0.03474592 0.0005908043
## 208   208 0.03249686 0.1990829 0.02492739 0.0008758180 0.03471911 0.0005886337
## 209   209 0.03249806 0.1990351 0.02492811 0.0008743648 0.03465560 0.0005880437
## 210   210 0.03249678 0.1990961 0.02492827 0.0008739620 0.03463195 0.0005884302
## 211   211 0.03249666 0.1990965 0.02492926 0.0008748057 0.03466463 0.0005888852
## 212   212 0.03249713 0.1990703 0.02492857 0.0008751715 0.03464105 0.0005900112
## 213   213 0.03249735 0.1990601 0.02492847 0.0008754028 0.03463836 0.0005904566
## 214   214 0.03249683 0.1990798 0.02492931 0.0008746378 0.03454403 0.0005900086
## 215   215 0.03249741 0.1990594 0.02492879 0.0008751510 0.03453079 0.0005909715
## 216   216 0.03249792 0.1990439 0.02492824 0.0008752641 0.03452670 0.0005917436
## 217   217 0.03249738 0.1990614 0.02492745 0.0008752139 0.03450778 0.0005904128
## 218   218 0.03249877 0.1990066 0.02492862 0.0008757781 0.03449711 0.0005906042
## 219   219 0.03249911 0.1989887 0.02492877 0.0008756685 0.03447755 0.0005902879
## 220   220 0.03249969 0.1989647 0.02492930 0.0008755146 0.03444921 0.0005898006
## 221   221 0.03249966 0.1989690 0.02492888 0.0008759477 0.03447460 0.0005896631
## 222   222 0.03249987 0.1989670 0.02492902 0.0008754698 0.03450162 0.0005897607
## 223   223 0.03249982 0.1989739 0.02492932 0.0008756809 0.03452805 0.0005894229
## 224   224 0.03250048 0.1989442 0.02492961 0.0008750176 0.03448473 0.0005889142
## 225   225 0.03250152 0.1989007 0.02492986 0.0008742688 0.03447501 0.0005895298
## 226   226 0.03250154 0.1988985 0.02493019 0.0008751578 0.03452779 0.0005899196
## 227   227 0.03250120 0.1989146 0.02493008 0.0008746615 0.03453660 0.0005894590
## 228   228 0.03250117 0.1989154 0.02493019 0.0008744490 0.03450365 0.0005893487
## 229   229 0.03250138 0.1989092 0.02493076 0.0008748681 0.03450909 0.0005898006
## 230   230 0.03250202 0.1988837 0.02493127 0.0008753845 0.03451525 0.0005907059
## 231   231 0.03250174 0.1988955 0.02493155 0.0008752620 0.03453263 0.0005906768
## 232   232 0.03250172 0.1988959 0.02493129 0.0008753881 0.03455645 0.0005909734
## 233   233 0.03250199 0.1988857 0.02493163 0.0008752934 0.03453992 0.0005910003
## 234   234 0.03250185 0.1988908 0.02493129 0.0008752629 0.03453640 0.0005907534
## 235   235 0.03250217 0.1988765 0.02493170 0.0008753765 0.03453248 0.0005912316
## 236   236 0.03250231 0.1988701 0.02493181 0.0008753587 0.03452230 0.0005914375
## 237   237 0.03250231 0.1988711 0.02493180 0.0008753858 0.03452655 0.0005915679
## 238   238 0.03250246 0.1988655 0.02493188 0.0008753904 0.03452419 0.0005916808
## 239   239 0.03250247 0.1988651 0.02493187 0.0008753765 0.03452171 0.0005917486
## 240   240 0.03250253 0.1988622 0.02493193 0.0008752879 0.03451534 0.0005917198
## [1] "Best Model"
##   nvmax
## 7     7

## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

## [1] "Coefficients of final model:"
##                  Estimate         2.5 %        97.5 %
## (Intercept)  2.010989e+00  2.005707e+00  2.016270e+00
## x4          -4.399973e-05 -6.159867e-05 -2.640079e-05
## x7           1.108087e-02  9.833384e-03  1.232835e-02
## x9           3.310416e-03  2.662524e-03  3.958309e-03
## x17          1.507310e-03  8.723715e-04  2.142248e-03
## stat98       3.548406e-03  3.072152e-03  4.024661e-03
## stat110     -3.282208e-03 -3.767312e-03 -2.797105e-03
## x18.sqrt     2.527794e-02  2.342698e-02  2.712889e-02

======= ## Fitting nvmax = 13 on full training set ## [1] "All models results" ## nvmax RMSE Rsquared MAE RMSESD RsquaredSD MAESD ## 1 1 0.03385458 0.1096104 0.02634130 0.0008295538 0.02478797 0.0004982521 ## 2 2 0.03308589 0.1497922 0.02574921 0.0010157625 0.03247206 0.0005889199 ## 3 3 0.03249415 0.1799293 0.02517980 0.0010498661 0.03378978 0.0006072363 ## 4 4 0.03196165 0.2063363 0.02447506 0.0009342472 0.03165626 0.0004690114 ## 5 5 0.03171189 0.2187152 0.02429046 0.0009442026 0.03113072 0.0005214975 ## 6 6 0.03161733 0.2231860 0.02421222 0.0009393708 0.02922561 0.0005173032 ## 7 7 0.03160116 0.2241139 0.02422636 0.0009247879 0.02858110 0.0004891560 ## 8 8 0.03148146 0.2300943 0.02414098 0.0009244857 0.02881080 0.0004732991 ## 9 9 0.03148587 0.2299594 0.02416144 0.0009477416 0.02913802 0.0004982399 ## 10 10 0.03148711 0.2298547 0.02415440 0.0009739512 0.02987084 0.0005053064 ## 11 11 0.03148089 0.2301187 0.02416120 0.0009953110 0.02990456 0.0005364930 ## 12 12 0.03148470 0.2299522 0.02416349 0.0009990068 0.02944639 0.0005495697 ## 13 13 0.03145749 0.2311967 0.02414219 0.0009791909 0.02841144 0.0005384081 ## 14 14 0.03147437 0.2303786 0.02416961 0.0009806357 0.02822536 0.0005623535 ## 15 15 0.03146569 0.2307427 0.02417507 0.0009936339 0.02783595 0.0005714702 ## 16 16 0.03148991 0.2296581 0.02420039 0.0009779886 0.02712579 0.0005488794 ## 17 17 0.03150643 0.2289046 0.02421673 0.0009893667 0.02727567 0.0005628079 ## 18 18 0.03149982 0.2292535 0.02420143 0.0009945389 0.02708799 0.0005689028 ## 19 19 0.03148965 0.2297416 0.02418990 0.0010067669 0.02740872 0.0005775336 ## 20 20 0.03148734 0.2299763 0.02421181 0.0010281631 0.02837203 0.0006011993 ## 21 21 0.03149039 0.2298256 0.02421445 0.0010305432 0.02825896 0.0005965495 ## 22 22 0.03149562 0.2296796 0.02421640 0.0010353947 0.02841205 0.0006094047 ## 23 23 0.03151241 0.2288523 0.02422678 0.0010342105 0.02796473 0.0006113076 ## 24 24 0.03150123 0.2293981 0.02421464 0.0010382557 0.02814206 0.0006112747 ## 25 25 0.03150030 0.2294055 0.02421937 0.0010259090 0.02723670 0.0006036940 ## 26 26 0.03148503 0.2301484 0.02421383 0.0010383896 0.02784105 0.0006018764 ## 27 27 0.03148870 0.2299910 0.02421166 0.0010409668 0.02805096 0.0006223322 ## 28 28 0.03149164 0.2298689 0.02421446 0.0010475865 0.02817762 0.0006217105 ## 29 29 0.03150762 0.2291131 0.02423181 0.0010454282 0.02854621 0.0006274450 ## 30 30 0.03150194 0.2294108 0.02421748 0.0010356148 0.02873647 0.0006150540 ## 31 31 0.03152398 0.2284308 0.02422189 0.0010229984 0.02839326 0.0005956601 ## 32 32 0.03152726 0.2282500 0.02423046 0.0010176376 0.02821051 0.0005934954 ## 33 33 0.03152665 0.2283797 0.02423569 0.0010279635 0.02893915 0.0006031575 ## 34 34 0.03151796 0.2287626 0.02422206 0.0010203039 0.02871491 0.0005815572 ## 35 35 0.03152188 0.2286335 0.02421730 0.0010328349 0.02996362 0.0005969662 ## 36 36 0.03151609 0.2289389 0.02420336 0.0010522874 0.03060404 0.0005997562 ## 37 37 0.03153971 0.2278691 0.02421355 0.0010513591 0.03040757 0.0006061880 ## 38 38 0.03152108 0.2287407 0.02420077 0.0010539417 0.03086271 0.0006036952 ## 39 39 0.03154157 0.2278284 0.02421705 0.0010635866 0.03097179 0.0006032555 ## 40 40 0.03154767 0.2275729 0.02422286 0.0010903027 0.03158575 0.0006327650 ## 41 41 0.03156603 0.2266967 0.02423231 0.0010887132 0.03168584 0.0006300055 ## 42 42 0.03158288 0.2259341 0.02425113 0.0010921414 0.03163684 0.0006311692 ## 43 43 0.03159212 0.2255308 0.02425169 0.0010906894 0.03155566 0.0006225412 ## 44 44 0.03160760 0.2248204 0.02426772 0.0010926506 0.03128084 0.0006181163 ## 45 45 0.03161962 0.2243067 0.02427944 0.0011005990 0.03134491 0.0006129422 ## 46 46 0.03163727 0.2235394 0.02428605 0.0010961284 0.03125069 0.0006144160 ## 47 47 0.03165256 0.2228692 0.02429918 0.0010894147 0.03069431 0.0006165416 ## 48 48 0.03168448 0.2214048 0.02433259 0.0010861216 0.03052200 0.0006092059 ## 49 49 0.03168228 0.2215498 0.02433165 0.0011059340 0.03156581 0.0006256120 ## 50 50 0.03169873 0.2207926 0.02433367 0.0011040089 0.03138761 0.0006304474 ## 51 51 0.03170625 0.2205027 0.02434531 0.0011125692 0.03152805 0.0006261585 ## 52 52 0.03172888 0.2195189 0.02436345 0.0011210757 0.03190875 0.0006326619 ## 53 53 0.03173833 0.2191255 0.02437395 0.0011227931 0.03201558 0.0006229525 ## 54 54 0.03173091 0.2195036 0.02437030 0.0011309028 0.03231791 0.0006414506 ## 55 55 0.03175009 0.2186384 0.02437952 0.0011207532 0.03211231 0.0006263079 ## 56 56 0.03177631 0.2174751 0.02440000 0.0011298996 0.03218819 0.0006298855 ## 57 57 0.03179105 0.2168322 0.02441954 0.0011327483 0.03239828 0.0006311695 ## 58 58 0.03179543 0.2166167 0.02441551 0.0011226956 0.03194527 0.0006248217 ## 59 59 0.03179682 0.2165954 0.02441419 0.0011132396 0.03136437 0.0006204672 ## 60 60 0.03180899 0.2160667 0.02442704 0.0011158744 0.03151877 0.0006271045 ## 61 61 0.03181399 0.2158287 0.02443812 0.0011170225 0.03166624 0.0006187309 ## 62 62 0.03182950 0.2151802 0.02445959 0.0011207396 0.03164840 0.0006338023 ## 63 63 0.03183159 0.2150761 0.02446088 0.0011141326 0.03147101 0.0006301800 ## 64 64 0.03183710 0.2148396 0.02446407 0.0011021557 0.03087915 0.0006181052 ## 65 65 0.03184674 0.2144377 0.02447586 0.0010948741 0.03065578 0.0006072468 ## 66 66 0.03184914 0.2143324 0.02447817 0.0010910051 0.03040860 0.0006095775 ## 67 67 0.03184564 0.2145554 0.02447919 0.0011023150 0.03091561 0.0006222728 ## 68 68 0.03184676 0.2145530 0.02448316 0.0011039506 0.03104141 0.0006164407 ## 69 69 0.03184237 0.2147087 0.02448071 0.0010965171 0.03086172 0.0006175814 ## 70 70 0.03183447 0.2151060 0.02447435 0.0011013035 0.03068614 0.0006185848 ## 71 71 0.03183614 0.2150547 0.02447275 0.0011129815 0.03074796 0.0006288891 ## 72 72 0.03184422 0.2147404 0.02448480 0.0011134711 0.03095384 0.0006268541 ## 73 73 0.03186211 0.2139748 0.02450351 0.0011112713 0.03063664 0.0006279500 ## 74 74 0.03186912 0.2137213 0.02451864 0.0011178984 0.03088926 0.0006297621 ## 75 75 0.03188033 0.2133161 0.02452957 0.0011354314 0.03190261 0.0006408760 ## 76 76 0.03189291 0.2127628 0.02454267 0.0011419099 0.03193809 0.0006482512 ## 77 77 0.03189488 0.2126862 0.02454392 0.0011294984 0.03129447 0.0006364631 ## 78 78 0.03190201 0.2123742 0.02454723 0.0011381035 0.03155580 0.0006367078 ## 79 79 0.03189664 0.2126411 0.02453894 0.0011454135 0.03185436 0.0006396544 ## 80 80 0.03190974 0.2120906 0.02454493 0.0011522273 0.03222378 0.0006508030 ## 81 81 0.03191369 0.2119374 0.02454340 0.0011595066 0.03230649 0.0006553162 ## 82 82 0.03191874 0.2117034 0.02454972 0.0011578958 0.03201588 0.0006556645 ## 83 83 0.03192325 0.2115324 0.02455813 0.0011465857 0.03170870 0.0006432353 ## 84 84 0.03193218 0.2111023 0.02455917 0.0011379002 0.03128737 0.0006367204 ## 85 85 0.03194500 0.2105574 0.02457105 0.0011367092 0.03109805 0.0006391154 ## 86 86 0.03194854 0.2104327 0.02457569 0.0011424890 0.03130890 0.0006436462 ## 87 87 0.03195029 0.2103709 0.02457721 0.0011355757 0.03104367 0.0006398209 ## 88 88 0.03194445 0.2106402 0.02457548 0.0011282636 0.03081283 0.0006468699 ## 89 89 0.03195891 0.2100413 0.02458663 0.0011272111 0.03068918 0.0006430510 ## 90 90 0.03195401 0.2102664 0.02457459 0.0011397955 0.03124134 0.0006584990 ## 91 91 0.03196393 0.2098952 0.02457780 0.0011390448 0.03124107 0.0006572308 ## 92 92 0.03197206 0.2095377 0.02458189 0.0011316200 0.03099955 0.0006560113 ## 93 93 0.03198363 0.2091021 0.02458806 0.0011300113 0.03087385 0.0006599111 ## 94 94 0.03198373 0.2091618 0.02458885 0.0011258313 0.03073495 0.0006544332 ## 95 95 0.03198670 0.2090266 0.02459468 0.0011248481 0.03083401 0.0006528552 ## 96 96 0.03198783 0.2089614 0.02459973 0.0011251973 0.03087446 0.0006562168 ## 97 97 0.03198701 0.2090226 0.02459331 0.0011293460 0.03119994 0.0006621649 ## 98 98 0.03200057 0.2085114 0.02459744 0.0011333184 0.03124247 0.0006674357 ## 99 99 0.03199983 0.2085464 0.02459378 0.0011410863 0.03154115 0.0006694835 ## 100 100 0.03199238 0.2088706 0.02458552 0.0011424034 0.03146923 0.0006790156 ## 101 101 0.03199740 0.2086912 0.02458649 0.0011506824 0.03185690 0.0006886233 ## 102 102 0.03200290 0.2084651 0.02459492 0.0011503489 0.03177499 0.0006795861 ## 103 103 0.03200293 0.2084787 0.02459540 0.0011499730 0.03185931 0.0006767545 ## 104 104 0.03200354 0.2084457 0.02459592 0.0011451080 0.03151677 0.0006740884 ## 105 105 0.03200601 0.2083357 0.02459645 0.0011443595 0.03151951 0.0006806581 ## 106 106 0.03200619 0.2083268 0.02459972 0.0011402674 0.03140935 0.0006821767 ## 107 107 0.03201305 0.2080327 0.02460193 0.0011316479 0.03112423 0.0006722950 ## 108 108 0.03201378 0.2080112 0.02459436 0.0011285986 0.03112527 0.0006694736 ## 109 109 0.03201712 0.2078442 0.02459618 0.0011291006 0.03116477 0.0006703776 ## 110 110 0.03201495 0.2079198 0.02459509 0.0011301334 0.03123062 0.0006694449 ## 111 111 0.03201965 0.2077687 0.02459770 0.0011378391 0.03158282 0.0006741437 ## 112 112 0.03202471 0.2075414 0.02460269 0.0011457676 0.03191216 0.0006817749 ## 113 113 0.03202648 0.2074941 0.02460188 0.0011489600 0.03206860 0.0006859216 ## 114 114 0.03202953 0.2073788 0.02460383 0.0011459513 0.03205737 0.0006875130 ## 115 115 0.03203220 0.2072700 0.02460418 0.0011413245 0.03178745 0.0006817709 ## 116 116 0.03203835 0.2070403 0.02461206 0.0011478424 0.03196953 0.0006858353 ## 117 117 0.03204683 0.2066827 0.02461840 0.0011425950 0.03168421 0.0006822265 ## 118 118 0.03204732 0.2066729 0.02461901 0.0011407043 0.03150565 0.0006756305 ## 119 119 0.03204971 0.2065697 0.02462174 0.0011438415 0.03168880 0.0006764938 ## 120 120 0.03205113 0.2064778 0.02462514 0.0011429186 0.03164883 0.0006814383 ## 121 121 0.03205458 0.2063379 0.02462764 0.0011347764 0.03136545 0.0006741159 ## 122 122 0.03205379 0.2064090 0.02462672 0.0011419756 0.03174433 0.0006778833 ## 123 123 0.03205280 0.2064513 0.02462466 0.0011409645 0.03165798 0.0006759197 ## 124 124 0.03205283 0.2064593 0.02462716 0.0011424141 0.03165763 0.0006747770 ## 125 125 0.03204920 0.2066213 0.02462665 0.0011383507 0.03140319 0.0006754891 ## 126 126 0.03204892 0.2066330 0.02462417 0.0011359859 0.03137349 0.0006717698 ## 127 127 0.03205096 0.2065761 0.02462625 0.0011334792 0.03124219 0.0006719293 ## 128 128 0.03205645 0.2063443 0.02462976 0.0011300527 0.03101835 0.0006671213 ## 129 129 0.03205879 0.2062567 0.02462930 0.0011301412 0.03111591 0.0006624874 ## 130 130 0.03205753 0.2063390 0.02462912 0.0011302508 0.03110370 0.0006588343 ## 131 131 0.03205997 0.2062352 0.02463451 0.0011241991 0.03079557 0.0006539486 ## 132 132 0.03205856 0.2063145 0.02463140 0.0011217790 0.03083442 0.0006522461 ## 133 133 0.03205798 0.2063390 0.02463891 0.0011160781 0.03054042 0.0006439798 ## 134 134 0.03206229 0.2061494 0.02464216 0.0011084869 0.03030594 0.0006387108 ## 135 135 0.03206697 0.2059970 0.02464547 0.0011174011 0.03077732 0.0006470535 ## 136 136 0.03207088 0.2058289 0.02464527 0.0011136306 0.03050577 0.0006467751 ## 137 137 0.03206913 0.2059006 0.02464778 0.0011162843 0.03058968 0.0006493711 ## 138 138 0.03207566 0.2056283 0.02465507 0.0011155473 0.03050247 0.0006454265 ## 139 139 0.03207207 0.2057647 0.02465389 0.0011098581 0.03032386 0.0006436001 ## 140 140 0.03207425 0.2056548 0.02465289 0.0011060018 0.03012625 0.0006449472 ## 141 141 0.03207457 0.2056452 0.02465251 0.0011009955 0.02985444 0.0006401691 ## 142 142 0.03207430 0.2056877 0.02464867 0.0011019350 0.02992069 0.0006385963 ## 143 143 0.03207330 0.2057283 0.02465038 0.0011014990 0.02994517 0.0006379622 ## 144 144 0.03207869 0.2054839 0.02465693 0.0011012916 0.02978443 0.0006390892 ## 145 145 0.03208088 0.2053861 0.02465703 0.0010998213 0.02974541 0.0006392672 ## 146 146 0.03208617 0.2051485 0.02466174 0.0010894836 0.02946710 0.0006292576 ## 147 147 0.03208623 0.2051495 0.02466201 0.0010854575 0.02932436 0.0006237219 ## 148 148 0.03208837 0.2050509 0.02466133 0.0010846587 0.02937443 0.0006207047 ## 149 149 0.03209227 0.2048878 0.02466114 0.0010827812 0.02937854 0.0006196246 ## 150 150 0.03209235 0.2048965 0.02466248 0.0010859355 0.02961160 0.0006251434 ## 151 151 0.03209245 0.2048823 0.02466068 0.0010828886 0.02959406 0.0006226528 ## 152 152 0.03209325 0.2048546 0.02466501 0.0010802333 0.02953837 0.0006197364 ## 153 153 0.03209090 0.2049578 0.02466355 0.0010855734 0.02969854 0.0006271767 ## 154 154 0.03208952 0.2050289 0.02466287 0.0010884877 0.02982372 0.0006272511 ## 155 155 0.03208979 0.2050039 0.02466090 0.0010894040 0.02978673 0.0006321751 ## 156 156 0.03208433 0.2052513 0.02465435 0.0010910820 0.02980501 0.0006325861 ## 157 157 0.03208190 0.2053705 0.02465184 0.0010909230 0.02993580 0.0006302241 ## 158 158 0.03208610 0.2051970 0.02465539 0.0010869471 0.02978380 0.0006280394 ## 159 159 0.03208514 0.2052309 0.02465376 0.0010891107 0.02983277 0.0006329842 ## 160 160 0.03208289 0.2053362 0.02465299 0.0010927928 0.03004625 0.0006351613 ## 161 161 0.03208513 0.2052390 0.02465399 0.0010980524 0.03025764 0.0006376889 ## 162 162 0.03208405 0.2053007 0.02465445 0.0010976436 0.03018810 0.0006390775 ## 163 163 0.03208477 0.2052721 0.02465539 0.0010965207 0.03017224 0.0006374807 ## 164 164 0.03208412 0.2052951 0.02465331 0.0010972946 0.03017178 0.0006393013 ## 165 165 0.03208396 0.2052955 0.02465313 0.0010918313 0.02998144 0.0006336088 ## 166 166 0.03208676 0.2051612 0.02465231 0.0010935109 0.02993785 0.0006348755 ## 167 167 0.03208535 0.2052329 0.02464830 0.0010959251 0.03007276 0.0006384679 ## 168 168 0.03208659 0.2051887 0.02464848 0.0010984508 0.03011117 0.0006447972 ## 169 169 0.03208937 0.2050761 0.02465251 0.0010998241 0.03015737 0.0006476004 ## 170 170 0.03209079 0.2050040 0.02465524 0.0011001584 0.03011193 0.0006479421 ## 171 171 0.03209271 0.2049418 0.02465569 0.0010978292 0.03005729 0.0006473847 ## 172 172 0.03209099 0.2050176 0.02465418 0.0010973456 0.03002143 0.0006472052 ## 173 173 0.03209149 0.2049835 0.02465410 0.0010967600 0.02991083 0.0006481944 ## 174 174 0.03209094 0.2050143 0.02465250 0.0010976032 0.02997440 0.0006470378 ## 175 175 0.03209169 0.2049752 0.02465102 0.0010980381 0.03003935 0.0006487678 ## 176 176 0.03209213 0.2049613 0.02465105 0.0010974598 0.03002888 0.0006465534 ## 177 177 0.03209028 0.2050431 0.02465094 0.0011005006 0.03020171 0.0006501054 ## 178 178 0.03209304 0.2049288 0.02465458 0.0010984931 0.03013958 0.0006460770 ## 179 179 0.03209457 0.2048692 0.02465697 0.0010981838 0.03014507 0.0006455129 ## 180 180 0.03209880 0.2047040 0.02465897 0.0010989862 0.03025039 0.0006453711 ## 181 181 0.03210165 0.2045977 0.02466056 0.0011017504 0.03040096 0.0006438785 ## 182 182 0.03210273 0.2045482 0.02466128 0.0011014313 0.03031420 0.0006429578 ## 183 183 0.03210347 0.2045247 0.02466139 0.0010988375 0.03026955 0.0006406877 ## 184 184 0.03210589 0.2044271 0.02466273 0.0011036727 0.03043728 0.0006457711 ## 185 185 0.03210597 0.2044257 0.02466181 0.0011037167 0.03040910 0.0006433408 ## 186 186 0.03210420 0.2044988 0.02465811 0.0011051202 0.03050014 0.0006454520 ## 187 187 0.03210761 0.2043523 0.02465953 0.0011051731 0.03045573 0.0006443201 ## 188 188 0.03210787 0.2043398 0.02466063 0.0011032304 0.03033105 0.0006435954 ## 189 189 0.03210751 0.2043498 0.02466154 0.0011040544 0.03029245 0.0006436060 ## 190 190 0.03210826 0.2043220 0.02466446 0.0011035717 0.03030565 0.0006430880 ## 191 191 0.03210572 0.2044321 0.02466306 0.0011056422 0.03038783 0.0006429226 ## 192 192 0.03210889 0.2042929 0.02466381 0.0011051824 0.03039140 0.0006419025 ## 193 193 0.03210620 0.2044115 0.02466275 0.0011069860 0.03042055 0.0006446823 ## 194 194 0.03210662 0.2044012 0.02466316 0.0011045390 0.03039443 0.0006426465 ## 195 195 0.03210861 0.2043164 0.02466373 0.0011033651 0.03033653 0.0006406348 ## 196 196 0.03210911 0.2042810 0.02466371 0.0011022041 0.03027123 0.0006392670 ## 197 197 0.03211217 0.2041458 0.02466584 0.0011026077 0.03028297 0.0006385982 ## 198 198 0.03211090 0.2041969 0.02466462 0.0011029133 0.03028177 0.0006387208 ## 199 199 0.03211312 0.2041006 0.02466644 0.0011029932 0.03025385 0.0006398724 ## 200 200 0.03211128 0.2041760 0.02466705 0.0011031607 0.03021799 0.0006397630 ## 201 201 0.03211183 0.2041562 0.02466698 0.0011036281 0.03023200 0.0006380779 ## 202 202 0.03211063 0.2042118 0.02466758 0.0011033300 0.03021874 0.0006381737 ## 203 203 0.03211102 0.2041871 0.02466820 0.0011034352 0.03016556 0.0006388333 ## 204 204 0.03210900 0.2042772 0.02466674 0.0011043321 0.03024071 0.0006381471 ## 205 205 0.03210899 0.2042789 0.02466674 0.0011040811 0.03019419 0.0006379155 ## 206 206 0.03210925 0.2042731 0.02466675 0.0011048055 0.03021223 0.0006396567 ## 207 207 0.03210745 0.2043563 0.02466516 0.0011046420 0.03023213 0.0006407044 ## 208 208 0.03210729 0.2043615 0.02466463 0.0011054014 0.03024237 0.0006412264 ## 209 209 0.03210924 0.2042686 0.02466627 0.0011054587 0.03023173 0.0006415652 ## 210 210 0.03210940 0.2042757 0.02466676 0.0011074000 0.03032859 0.0006436772 ## 211 211 0.03210883 0.2042997 0.02466565 0.0011078063 0.03033795 0.0006444732 ## 212 212 0.03210970 0.2042682 0.02466706 0.0011075618 0.03033605 0.0006448931 ## 213 213 0.03210888 0.2042934 0.02466580 0.0011065718 0.03030064 0.0006435122 ## 214 214 0.03210762 0.2043480 0.02466444 0.0011066733 0.03028133 0.0006446942 ## 215 215 0.03210922 0.2042785 0.02466503 0.0011074218 0.03028543 0.0006460986 ## 216 216 0.03211078 0.2042151 0.02466665 0.0011067384 0.03026335 0.0006449334 ## 217 217 0.03211109 0.2042072 0.02466717 0.0011092032 0.03036328 0.0006470520 ## 218 218 0.03211111 0.2042070 0.02466656 0.0011089075 0.03033337 0.0006467482 ## 219 219 0.03211051 0.2042295 0.02466618 0.0011083204 0.03031500 0.0006466827 ## 220 220 0.03211076 0.2042154 0.02466654 0.0011077153 0.03028606 0.0006450397 ## 221 221 0.03211001 0.2042474 0.02466652 0.0011080025 0.03032290 0.0006449498 ## 222 222 0.03211061 0.2042185 0.02466710 0.0011079167 0.03033603 0.0006443065 ## 223 223 0.03210918 0.2042743 0.02466632 0.0011072305 0.03030832 0.0006432578 ## 224 224 0.03210988 0.2042473 0.02466727 0.0011072034 0.03032871 0.0006428482 ## 225 225 0.03210996 0.2042470 0.02466728 0.0011070552 0.03031321 0.0006424427 ## 226 226 0.03211009 0.2042409 0.02466757 0.0011074967 0.03033923 0.0006428487 ## 227 227 0.03211021 0.2042403 0.02466787 0.0011081142 0.03039217 0.0006430474 ## 228 228 0.03210967 0.2042650 0.02466704 0.0011083854 0.03039150 0.0006432076 ## 229 229 0.03210983 0.2042598 0.02466729 0.0011091435 0.03042026 0.0006439666 ## 230 230 0.03210963 0.2042692 0.02466754 0.0011094325 0.03042553 0.0006438673 ## 231 231 0.03210959 0.2042718 0.02466768 0.0011091845 0.03042081 0.0006433408 ## 232 232 0.03211034 0.2042399 0.02466868 0.0011088124 0.03040087 0.0006427493 ## 233 233 0.03211031 0.2042421 0.02466841 0.0011094963 0.03043202 0.0006434366 ## 234 234 0.03211014 0.2042491 0.02466836 0.0011092755 0.03042107 0.0006430091 ## 235 235 0.03211022 0.2042449 0.02466844 0.0011091303 0.03041803 0.0006434017 ## 236 236 0.03210982 0.2042631 0.02466832 0.0011092561 0.03042793 0.0006437501 ## 237 237 0.03210997 0.2042566 0.02466848 0.0011088841 0.03040869 0.0006432413 ## 238 238 0.03210991 0.2042592 0.02466824 0.0011087237 0.03040023 0.0006431995 ## 239 239 0.03210989 0.2042603 0.02466821 0.0011087423 0.03039855 0.0006432065 ## 240 240 0.03210993 0.2042585 0.02466824 0.0011087027 0.03039707 0.0006431900 ## [1] "Best Model" ## nvmax ## 13 13

## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

## [1] "Coefficients of final model:"
##                  Estimate         2.5 %        97.5 %
## (Intercept)  1.972681e+00  1.956867e+00  1.988495e+00
## x4          -4.607173e-05 -6.334938e-05 -2.879408e-05
## x7           1.080812e-02  9.583611e-03  1.203263e-02
## x8           4.784756e-04  1.929724e-04  7.639787e-04
## x9           3.106132e-03  2.470605e-03  3.741659e-03
## x10          1.140634e-03  5.481000e-04  1.733168e-03
## x11          2.032330e+05  6.180148e+04  3.446645e+05
## x16          1.063749e-03  6.532151e-04  1.474284e-03
## x17          1.860411e-03  1.237166e-03  2.483656e-03
## stat14      -7.371136e-04 -1.207823e-03 -2.664039e-04
## stat41      -7.435917e-04 -1.216279e-03 -2.709043e-04
## stat98       3.577314e-03  3.108078e-03  4.046550e-03
## stat110     -3.392311e-03 -3.868431e-03 -2.916191e-03
## x18.sqrt     2.586108e-02  2.405283e-02  2.766932e-02

>>>>>>> 8e6f61bca4894b586983e20a3e14b1b8a049b903

Test

if (algo.forward.caret == TRUE){
    test.model(model=model.forward, test=data.test
             ,method = 'leapForward',subopt = NULL
             ,formula = formula, feature.names = feature.names, label.names = label.names
             ,id = id
             ,draw.limits = TRUE, transformation = t)
}

## [1] "Summary of predicted values: "
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
<<<<<<< HEAD
##   2.044   2.084   2.097   2.097   2.109   2.147 
## [1] "leapForward  Test MSE: 0.000942359887602509"

======= ## 2.039 2.084 2.097 2.097 2.109 2.145 ## [1] "leapForward Test MSE: 0.00104530808325543"

>>>>>>> 8e6f61bca4894b586983e20a3e14b1b8a049b903

Backward Elimination with CV

Train

if (algo.backward.caret == TRUE){
  set.seed(1)
  returned = train.caret.glmselect(formula = formula
                                   ,data =  data.train
                                   ,method = "leapBackward"
                                   ,feature.names =  feature.names)
  model.backward = returned$model
  id = returned$id
}

## Aggregating results
## Selecting tuning parameters
<<<<<<< HEAD
## Fitting nvmax = 7 on full training set
## [1] "All models results"
##     nvmax       RMSE  Rsquared        MAE       RMSESD RsquaredSD        MAESD
## 1       1 0.03425332 0.1038025 0.02663970 0.0006637466 0.02345731 0.0004078960
## 2       2 0.03345274 0.1456791 0.02595410 0.0006744402 0.02299972 0.0005397020
## 3       3 0.03287356 0.1755708 0.02542164 0.0007428313 0.03453720 0.0006065015
## 4       4 0.03238568 0.2002338 0.02476762 0.0007588086 0.03652502 0.0005318967
## 5       5 0.03210370 0.2138463 0.02455180 0.0007501264 0.03860748 0.0004926778
## 6       6 0.03207281 0.2152005 0.02457183 0.0007522223 0.03774776 0.0004857396
## 7       7 0.03198024 0.2196041 0.02449315 0.0007733914 0.03745117 0.0004793219
## 8       8 0.03202042 0.2177381 0.02451834 0.0007986437 0.03807747 0.0004689433
## 9       9 0.03202975 0.2172467 0.02453799 0.0008229237 0.03807716 0.0004777837
## 10     10 0.03204470 0.2166573 0.02458335 0.0008692181 0.03928587 0.0004970027
## 11     11 0.03205450 0.2163469 0.02459478 0.0008900320 0.04095855 0.0005215186
## 12     12 0.03202978 0.2176650 0.02459328 0.0009083095 0.04241137 0.0005532378
## 13     13 0.03203789 0.2172484 0.02458580 0.0009255880 0.04316006 0.0005482828
## 14     14 0.03201746 0.2181256 0.02456640 0.0009074620 0.04320969 0.0005352318
## 15     15 0.03200221 0.2187415 0.02456541 0.0008875529 0.04192161 0.0005198344
## 16     16 0.03200929 0.2183536 0.02456633 0.0008841716 0.04062908 0.0005175875
## 17     17 0.03201623 0.2179853 0.02457879 0.0008811756 0.04097910 0.0005060063
## 18     18 0.03201548 0.2181183 0.02457520 0.0008755563 0.04167981 0.0005176730
## 19     19 0.03201459 0.2181521 0.02457154 0.0008561828 0.04113889 0.0005097624
## 20     20 0.03202603 0.2176078 0.02457884 0.0008480833 0.03917978 0.0005005236
## 21     21 0.03202865 0.2176383 0.02459647 0.0008657724 0.04060881 0.0005032706
## 22     22 0.03204473 0.2169285 0.02459972 0.0008469533 0.04085003 0.0004937527
## 23     23 0.03206098 0.2162634 0.02460930 0.0008841281 0.04174735 0.0005099297
## 24     24 0.03208911 0.2149458 0.02463996 0.0008641596 0.04142237 0.0005120474
## 25     25 0.03210544 0.2142768 0.02465212 0.0008646829 0.04140997 0.0005120867
## 26     26 0.03212017 0.2137234 0.02466389 0.0008634894 0.04206252 0.0005121214
## 27     27 0.03213479 0.2130040 0.02466578 0.0008519501 0.04047248 0.0005036940
## 28     28 0.03216692 0.2116068 0.02469126 0.0008543654 0.04077600 0.0005076495
## 29     29 0.03218570 0.2107178 0.02470522 0.0008509819 0.04080542 0.0005245350
## 30     30 0.03219028 0.2104525 0.02469786 0.0008407803 0.03991562 0.0005158468
## 31     31 0.03221768 0.2092514 0.02472540 0.0008349268 0.03976746 0.0005129946
## 32     32 0.03223220 0.2086308 0.02474066 0.0008400335 0.04001872 0.0005083977
## 33     33 0.03223634 0.2084468 0.02474432 0.0008228124 0.03922738 0.0004941479
## 34     34 0.03225122 0.2077992 0.02475405 0.0008217371 0.03876795 0.0004893599
## 35     35 0.03225900 0.2074829 0.02475287 0.0008240531 0.03941395 0.0005040681
## 36     36 0.03227544 0.2067578 0.02477485 0.0008179787 0.03915783 0.0004770500
## 37     37 0.03225675 0.2077521 0.02474526 0.0008476396 0.04054152 0.0004928211
## 38     38 0.03225720 0.2077773 0.02474213 0.0008406734 0.04016182 0.0005050043
## 39     39 0.03226090 0.2075128 0.02474110 0.0008313780 0.03957226 0.0005042573
## 40     40 0.03227245 0.2069610 0.02475569 0.0008220915 0.03888785 0.0005047208
## 41     41 0.03229145 0.2061642 0.02476215 0.0008071155 0.03882902 0.0004977170
## 42     42 0.03230389 0.2055462 0.02477372 0.0007907677 0.03782580 0.0004763453
## 43     43 0.03229428 0.2060093 0.02476251 0.0007955331 0.03733335 0.0004668917
## 44     44 0.03229774 0.2058901 0.02476817 0.0008039186 0.03743932 0.0004687772
## 45     45 0.03229504 0.2060363 0.02476530 0.0008067735 0.03725978 0.0004629515
## 46     46 0.03230076 0.2059024 0.02475716 0.0008044798 0.03791314 0.0004724821
## 47     47 0.03230440 0.2057873 0.02475499 0.0007930073 0.03740394 0.0004803090
## 48     48 0.03230637 0.2058095 0.02475444 0.0008053698 0.03754047 0.0004912001
## 49     49 0.03230980 0.2057258 0.02475726 0.0007909394 0.03706898 0.0004944410
## 50     50 0.03231186 0.2056870 0.02475429 0.0008001669 0.03702126 0.0004965228
## 51     51 0.03231204 0.2057881 0.02475278 0.0008095080 0.03774652 0.0005116265
## 52     52 0.03230799 0.2059734 0.02474452 0.0008095869 0.03756263 0.0005168704
## 53     53 0.03230719 0.2060785 0.02473988 0.0008280382 0.03822082 0.0005263669
## 54     54 0.03232644 0.2052333 0.02475224 0.0008494328 0.03782618 0.0005381098
## 55     55 0.03231833 0.2056291 0.02474760 0.0008501996 0.03812664 0.0005485853
## 56     56 0.03231958 0.2055521 0.02475384 0.0008495129 0.03788766 0.0005484292
## 57     57 0.03232559 0.2053413 0.02475969 0.0008621589 0.03869276 0.0005631305
## 58     58 0.03233239 0.2051260 0.02476605 0.0008787821 0.03951827 0.0005823639
## 59     59 0.03232655 0.2054135 0.02475957 0.0008923738 0.03978438 0.0005972076
## 60     60 0.03233220 0.2051646 0.02476674 0.0008832325 0.03939827 0.0005872547
## 61     61 0.03233897 0.2049324 0.02478007 0.0008944670 0.03996221 0.0006041239
## 62     62 0.03233688 0.2050736 0.02478691 0.0008979559 0.03994090 0.0006066822
## 63     63 0.03233164 0.2053450 0.02477968 0.0009019015 0.04040472 0.0006099315
## 64     64 0.03234154 0.2049146 0.02478660 0.0009069066 0.04066563 0.0006116384
## 65     65 0.03233338 0.2053073 0.02478218 0.0009141948 0.04082183 0.0006226000
## 66     66 0.03233371 0.2053373 0.02478257 0.0009192748 0.04138004 0.0006298045
## 67     67 0.03234096 0.2050339 0.02478651 0.0009218462 0.04111801 0.0006310186
## 68     68 0.03233542 0.2052236 0.02477734 0.0009051178 0.04012101 0.0006082848
## 69     69 0.03234685 0.2047373 0.02478546 0.0009038962 0.03997937 0.0006183930
## 70     70 0.03234070 0.2050546 0.02478213 0.0009102601 0.04040365 0.0006240110
## 71     71 0.03233957 0.2051443 0.02477904 0.0009153793 0.04078713 0.0006340950
## 72     72 0.03234976 0.2046927 0.02478323 0.0009235398 0.04134618 0.0006473123
## 73     73 0.03235191 0.2046096 0.02478638 0.0009206058 0.04149670 0.0006459423
## 74     74 0.03235144 0.2046963 0.02478104 0.0009313752 0.04154318 0.0006494079
## 75     75 0.03235147 0.2046688 0.02477816 0.0009256366 0.04110153 0.0006353433
## 76     76 0.03236088 0.2043201 0.02477349 0.0009385307 0.04135852 0.0006362904
## 77     77 0.03236037 0.2043797 0.02476188 0.0009521149 0.04167495 0.0006404720
## 78     78 0.03235389 0.2046875 0.02476024 0.0009548929 0.04198551 0.0006442619
## 79     79 0.03235303 0.2047848 0.02475704 0.0009611994 0.04218681 0.0006530337
## 80     80 0.03236731 0.2041524 0.02476343 0.0009562034 0.04179720 0.0006519405
## 81     81 0.03237199 0.2039507 0.02476400 0.0009600472 0.04133866 0.0006626356
## 82     82 0.03235828 0.2045655 0.02476100 0.0009556789 0.04099425 0.0006601910
## 83     83 0.03235923 0.2045730 0.02476208 0.0009557336 0.04134538 0.0006645566
## 84     84 0.03235912 0.2045519 0.02476275 0.0009458908 0.04104955 0.0006556081
## 85     85 0.03235098 0.2048861 0.02474872 0.0009384398 0.04066529 0.0006426720
## 86     86 0.03236183 0.2044052 0.02476559 0.0009437937 0.04062132 0.0006505516
## 87     87 0.03237355 0.2038795 0.02478416 0.0009426925 0.04033215 0.0006592028
## 88     88 0.03237546 0.2038024 0.02479239 0.0009355022 0.03981017 0.0006533088
## 89     89 0.03237998 0.2036086 0.02479028 0.0009429903 0.03972077 0.0006543550
## 90     90 0.03238978 0.2032025 0.02479975 0.0009478051 0.03969487 0.0006506994
## 91     91 0.03238828 0.2033108 0.02480334 0.0009536522 0.04008011 0.0006581045
## 92     92 0.03239534 0.2030323 0.02480906 0.0009524306 0.03992626 0.0006514516
## 93     93 0.03240158 0.2027711 0.02481625 0.0009579399 0.04011574 0.0006548657
## 94     94 0.03241649 0.2020803 0.02482217 0.0009439169 0.03912853 0.0006477592
## 95     95 0.03241972 0.2018991 0.02483142 0.0009411456 0.03838384 0.0006448833
## 96     96 0.03242091 0.2017834 0.02483403 0.0009332973 0.03807143 0.0006407759
## 97     97 0.03242170 0.2017911 0.02484008 0.0009320744 0.03798944 0.0006471388
## 98     98 0.03241496 0.2020941 0.02483746 0.0009370558 0.03830581 0.0006491114
## 99     99 0.03241647 0.2020004 0.02484522 0.0009354085 0.03823085 0.0006526373
## 100   100 0.03241456 0.2020706 0.02484691 0.0009415328 0.03844397 0.0006550772
## 101   101 0.03241994 0.2018548 0.02485389 0.0009382804 0.03830023 0.0006529281
## 102   102 0.03242704 0.2015947 0.02485644 0.0009384459 0.03824000 0.0006535156
## 103   103 0.03242471 0.2016784 0.02485451 0.0009367696 0.03812976 0.0006516684
## 104   104 0.03242053 0.2018569 0.02484714 0.0009326418 0.03790233 0.0006432317
## 105   105 0.03243341 0.2013415 0.02486055 0.0009317135 0.03803062 0.0006472112
## 106   106 0.03244346 0.2008990 0.02486780 0.0009224619 0.03785437 0.0006410351
## 107   107 0.03244066 0.2010790 0.02486146 0.0009281954 0.03824324 0.0006460537
## 108   108 0.03243815 0.2011665 0.02486270 0.0009232100 0.03787161 0.0006415315
## 109   109 0.03243641 0.2012584 0.02486257 0.0009228068 0.03770281 0.0006354267
## 110   110 0.03243476 0.2013342 0.02485780 0.0009208155 0.03772985 0.0006318386
## 111   111 0.03244153 0.2010507 0.02486671 0.0009264927 0.03777319 0.0006347899
## 112   112 0.03244512 0.2008753 0.02487173 0.0009294150 0.03757041 0.0006301293
## 113   113 0.03244228 0.2009608 0.02487220 0.0009251368 0.03737047 0.0006229938
## 114   114 0.03243870 0.2011357 0.02487080 0.0009202326 0.03717711 0.0006153067
## 115   115 0.03244476 0.2008789 0.02487443 0.0009184403 0.03715169 0.0006140191
## 116   116 0.03244728 0.2007760 0.02488196 0.0009179865 0.03700468 0.0006074762
## 117   117 0.03244190 0.2010197 0.02488197 0.0009123737 0.03677916 0.0006016770
## 118   118 0.03244894 0.2007487 0.02488533 0.0009126452 0.03643658 0.0006046618
## 119   119 0.03243929 0.2011529 0.02487736 0.0009071571 0.03624164 0.0006079265
## 120   120 0.03244283 0.2010514 0.02488226 0.0009134660 0.03636106 0.0006180777
## 121   121 0.03244427 0.2010609 0.02488148 0.0009148976 0.03652459 0.0006174848
## 122   122 0.03244945 0.2008182 0.02488680 0.0009119308 0.03631945 0.0006128012
## 123   123 0.03245581 0.2005432 0.02488725 0.0009123385 0.03640731 0.0006085068
## 124   124 0.03245297 0.2006619 0.02489173 0.0009129194 0.03626959 0.0006145295
## 125   125 0.03244814 0.2008762 0.02488508 0.0009165463 0.03660155 0.0006133011
## 126   126 0.03244762 0.2009118 0.02488784 0.0009098030 0.03625566 0.0006051267
## 127   127 0.03245295 0.2006458 0.02489099 0.0009066927 0.03576490 0.0006002143
## 128   128 0.03244573 0.2009272 0.02488850 0.0009060542 0.03555825 0.0005987504
## 129   129 0.03245275 0.2006177 0.02489327 0.0009063281 0.03553632 0.0006061074
## 130   130 0.03245175 0.2006523 0.02489165 0.0009027759 0.03513428 0.0005963687
## 131   131 0.03245967 0.2002988 0.02489617 0.0009018495 0.03494414 0.0005934144
## 132   132 0.03246058 0.2002667 0.02489823 0.0008957945 0.03452913 0.0005892603
## 133   133 0.03246303 0.2001717 0.02490650 0.0008976344 0.03470926 0.0005907284
## 134   134 0.03247011 0.1998487 0.02491807 0.0009019086 0.03478751 0.0005893136
## 135   135 0.03247108 0.1998252 0.02492261 0.0008933055 0.03467518 0.0005911620
## 136   136 0.03248096 0.1994335 0.02492854 0.0008891232 0.03476535 0.0005869376
## 137   137 0.03248134 0.1994475 0.02492800 0.0008962226 0.03526829 0.0005927458
## 138   138 0.03247980 0.1995227 0.02492928 0.0008980769 0.03532209 0.0005924291
## 139   139 0.03247748 0.1996114 0.02492956 0.0008924741 0.03527879 0.0005867558
## 140   140 0.03247990 0.1995765 0.02492891 0.0008990298 0.03574933 0.0005914160
## 141   141 0.03248075 0.1995527 0.02492423 0.0008933510 0.03537442 0.0005885740
## 142   142 0.03248481 0.1994200 0.02492960 0.0009004975 0.03571308 0.0006001831
## 143   143 0.03248921 0.1992345 0.02492911 0.0008977155 0.03575133 0.0005950214
## 144   144 0.03248899 0.1992627 0.02493004 0.0008993493 0.03599085 0.0005995837
## 145   145 0.03248802 0.1993090 0.02493222 0.0008996267 0.03602325 0.0005959545
## 146   146 0.03248786 0.1993068 0.02493270 0.0008944526 0.03596578 0.0005929660
## 147   147 0.03248599 0.1993795 0.02493548 0.0008916145 0.03579382 0.0005953827
## 148   148 0.03248715 0.1993376 0.02493134 0.0008931865 0.03584547 0.0005965928
## 149   149 0.03247967 0.1996832 0.02492525 0.0008901702 0.03580308 0.0005953164
## 150   150 0.03248030 0.1996398 0.02492509 0.0008893478 0.03575191 0.0005953159
## 151   151 0.03247908 0.1996842 0.02492283 0.0008847148 0.03555972 0.0005934208
## 152   152 0.03247867 0.1997285 0.02492220 0.0008871653 0.03549270 0.0005951561
## 153   153 0.03247685 0.1998173 0.02491872 0.0008855208 0.03560468 0.0005882683
## 154   154 0.03247364 0.1999607 0.02491683 0.0008817312 0.03550499 0.0005835038
## 155   155 0.03247643 0.1998412 0.02491757 0.0008767824 0.03537080 0.0005809154
## 156   156 0.03247929 0.1997479 0.02491496 0.0008802024 0.03546313 0.0005863423
## 157   157 0.03247793 0.1997868 0.02491210 0.0008852722 0.03547960 0.0005882372
## 158   158 0.03247792 0.1997528 0.02490856 0.0008765300 0.03516350 0.0005830026
## 159   159 0.03248270 0.1995561 0.02491019 0.0008805917 0.03509420 0.0005857595
## 160   160 0.03248318 0.1995455 0.02491316 0.0008814192 0.03502038 0.0005856051
## 161   161 0.03248355 0.1995108 0.02491171 0.0008794684 0.03483803 0.0005797311
## 162   162 0.03248525 0.1994376 0.02491218 0.0008746398 0.03473257 0.0005787146
## 163   163 0.03248621 0.1994077 0.02491516 0.0008739026 0.03462654 0.0005826598
## 164   164 0.03248924 0.1992807 0.02491824 0.0008720160 0.03443113 0.0005792588
## 165   165 0.03249167 0.1991579 0.02492203 0.0008705328 0.03431573 0.0005766801
## 166   166 0.03248994 0.1992379 0.02492063 0.0008728192 0.03446324 0.0005742793
## 167   167 0.03248709 0.1993745 0.02491879 0.0008738200 0.03460814 0.0005754590
## 168   168 0.03248919 0.1993036 0.02491820 0.0008838534 0.03487807 0.0005838077
## 169   169 0.03248811 0.1993721 0.02491719 0.0008843275 0.03508555 0.0005833348
## 170   170 0.03248662 0.1994363 0.02491756 0.0008838456 0.03500095 0.0005835964
## 171   171 0.03248482 0.1995003 0.02491440 0.0008803264 0.03487570 0.0005846282
## 172   172 0.03248587 0.1994747 0.02491488 0.0008788198 0.03482278 0.0005840143
## 173   173 0.03248417 0.1995409 0.02491196 0.0008764807 0.03481496 0.0005801069
## 174   174 0.03248589 0.1994738 0.02491325 0.0008741659 0.03477782 0.0005798526
## 175   175 0.03248277 0.1996001 0.02491032 0.0008750532 0.03475663 0.0005782106
## 176   176 0.03248368 0.1995793 0.02491132 0.0008694755 0.03468218 0.0005744036
## 177   177 0.03248524 0.1995088 0.02491310 0.0008680756 0.03465088 0.0005747126
## 178   178 0.03248514 0.1995054 0.02491196 0.0008673279 0.03445212 0.0005773924
## 179   179 0.03248757 0.1994074 0.02491225 0.0008679335 0.03445758 0.0005740555
## 180   180 0.03248661 0.1994323 0.02491405 0.0008659456 0.03450038 0.0005732458
## 181   181 0.03248540 0.1994917 0.02491359 0.0008671068 0.03457182 0.0005745833
## 182   182 0.03248598 0.1994578 0.02491708 0.0008678656 0.03450642 0.0005771587
## 183   183 0.03248375 0.1995698 0.02491396 0.0008716514 0.03458035 0.0005795246
## 184   184 0.03248119 0.1996894 0.02491178 0.0008759805 0.03463431 0.0005797688
## 185   185 0.03248638 0.1994500 0.02491678 0.0008754796 0.03452164 0.0005769543
## 186   186 0.03248448 0.1995271 0.02491464 0.0008747700 0.03450348 0.0005784177
## 187   187 0.03248309 0.1995821 0.02491304 0.0008750297 0.03448864 0.0005776661
## 188   188 0.03248527 0.1994988 0.02491386 0.0008785071 0.03462768 0.0005825981
## 189   189 0.03248519 0.1994901 0.02491437 0.0008808105 0.03462460 0.0005838096
## 190   190 0.03248348 0.1995678 0.02491185 0.0008812150 0.03465522 0.0005834497
## 191   191 0.03248582 0.1994765 0.02491456 0.0008808687 0.03470206 0.0005834786
## 192   192 0.03248879 0.1993554 0.02491624 0.0008827440 0.03480037 0.0005832946
## 193   193 0.03248836 0.1993937 0.02491681 0.0008827079 0.03491264 0.0005871685
## 194   194 0.03249063 0.1993061 0.02491628 0.0008808992 0.03496958 0.0005889331
## 195   195 0.03249181 0.1992811 0.02491624 0.0008805230 0.03511208 0.0005900521
## 196   196 0.03249411 0.1991847 0.02491980 0.0008784703 0.03503171 0.0005888367
## 197   197 0.03249717 0.1990595 0.02492232 0.0008766760 0.03488136 0.0005876382
## 198   198 0.03249700 0.1990701 0.02492205 0.0008757393 0.03486623 0.0005874632
## 199   199 0.03249587 0.1991170 0.02492070 0.0008769262 0.03482918 0.0005868592
## 200   200 0.03249736 0.1990576 0.02492260 0.0008793085 0.03491794 0.0005910458
## 201   201 0.03249919 0.1989773 0.02492408 0.0008772338 0.03477848 0.0005881223
## 202   202 0.03249803 0.1990354 0.02492349 0.0008782833 0.03478624 0.0005909289
## 203   203 0.03249677 0.1990836 0.02492243 0.0008757856 0.03467841 0.0005860012
## 204   204 0.03249710 0.1990668 0.02492457 0.0008767562 0.03466324 0.0005860671
## 205   205 0.03249818 0.1990258 0.02492668 0.0008780947 0.03469432 0.0005871516
## 206   206 0.03249791 0.1990267 0.02492721 0.0008773839 0.03471409 0.0005887559
## 207   207 0.03249862 0.1990058 0.02492790 0.0008775362 0.03474592 0.0005908043
## 208   208 0.03249686 0.1990829 0.02492739 0.0008758180 0.03471911 0.0005886337
## 209   209 0.03249806 0.1990351 0.02492811 0.0008743648 0.03465560 0.0005880437
## 210   210 0.03249678 0.1990961 0.02492827 0.0008739620 0.03463195 0.0005884302
## 211   211 0.03249636 0.1991085 0.02492883 0.0008749114 0.03466904 0.0005890931
## 212   212 0.03249731 0.1990641 0.02492845 0.0008751065 0.03463876 0.0005900654
## 213   213 0.03249735 0.1990601 0.02492847 0.0008754028 0.03463836 0.0005904566
## 214   214 0.03249683 0.1990798 0.02492931 0.0008746378 0.03454403 0.0005900086
## 215   215 0.03249741 0.1990594 0.02492879 0.0008751510 0.03453079 0.0005909715
## 216   216 0.03249838 0.1990236 0.02492900 0.0008754930 0.03451170 0.0005912768
## 217   217 0.03249811 0.1990289 0.02492790 0.0008753197 0.03447562 0.0005900866
## 218   218 0.03249877 0.1990066 0.02492862 0.0008757781 0.03449711 0.0005906042
## 219   219 0.03249911 0.1989887 0.02492877 0.0008756685 0.03447755 0.0005902879
## 220   220 0.03249969 0.1989647 0.02492930 0.0008755146 0.03444921 0.0005898006
## 221   221 0.03249966 0.1989690 0.02492888 0.0008759477 0.03447460 0.0005896631
## 222   222 0.03249987 0.1989670 0.02492902 0.0008754698 0.03450162 0.0005897607
## 223   223 0.03249982 0.1989739 0.02492932 0.0008756809 0.03452805 0.0005894229
## 224   224 0.03250048 0.1989442 0.02492961 0.0008750176 0.03448473 0.0005889142
## 225   225 0.03250152 0.1989007 0.02492986 0.0008742688 0.03447501 0.0005895298
## 226   226 0.03250154 0.1988985 0.02493019 0.0008751578 0.03452779 0.0005899196
## 227   227 0.03250120 0.1989146 0.02493008 0.0008746615 0.03453660 0.0005894590
## 228   228 0.03250119 0.1989153 0.02493016 0.0008744449 0.03450364 0.0005893642
## 229   229 0.03250118 0.1989170 0.02493060 0.0008749421 0.03451212 0.0005898776
## 230   230 0.03250202 0.1988837 0.02493127 0.0008753845 0.03451525 0.0005907059
## 231   231 0.03250174 0.1988955 0.02493155 0.0008752620 0.03453263 0.0005906768
## 232   232 0.03250172 0.1988959 0.02493129 0.0008753881 0.03455645 0.0005909734
## 233   233 0.03250199 0.1988857 0.02493163 0.0008752934 0.03453992 0.0005910003
## 234   234 0.03250185 0.1988908 0.02493129 0.0008752629 0.03453640 0.0005907534
## 235   235 0.03250217 0.1988765 0.02493170 0.0008753765 0.03453248 0.0005912316
## 236   236 0.03250231 0.1988701 0.02493181 0.0008753587 0.03452230 0.0005914375
## 237   237 0.03250231 0.1988711 0.02493180 0.0008753858 0.03452655 0.0005915679
## 238   238 0.03250246 0.1988655 0.02493188 0.0008753904 0.03452419 0.0005916808
## 239   239 0.03250247 0.1988651 0.02493187 0.0008753765 0.03452171 0.0005917486
## 240   240 0.03250253 0.1988622 0.02493193 0.0008752879 0.03451534 0.0005917198
## [1] "Best Model"
##   nvmax
## 7     7

## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

## [1] "Coefficients of final model:"
##                  Estimate         2.5 %        97.5 %
## (Intercept)  2.010989e+00  2.005707e+00  2.016270e+00
## x4          -4.399973e-05 -6.159867e-05 -2.640079e-05
## x7           1.108087e-02  9.833384e-03  1.232835e-02
## x9           3.310416e-03  2.662524e-03  3.958309e-03
## x17          1.507310e-03  8.723715e-04  2.142248e-03
## stat98       3.548406e-03  3.072152e-03  4.024661e-03
## stat110     -3.282208e-03 -3.767312e-03 -2.797105e-03
## x18.sqrt     2.527794e-02  2.342698e-02  2.712889e-02

======= ## Fitting nvmax = 13 on full training set ## [1] "All models results" ## nvmax RMSE Rsquared MAE RMSESD RsquaredSD MAESD ## 1 1 0.03385458 0.1096104 0.02634130 0.0008295538 0.02478797 0.0004982521 ## 2 2 0.03308589 0.1497922 0.02574921 0.0010157625 0.03247206 0.0005889199 ## 3 3 0.03249415 0.1799293 0.02517980 0.0010498661 0.03378978 0.0006072363 ## 4 4 0.03196165 0.2063363 0.02447506 0.0009342472 0.03165626 0.0004690114 ## 5 5 0.03171189 0.2187152 0.02429046 0.0009442026 0.03113072 0.0005214975 ## 6 6 0.03161733 0.2231860 0.02421222 0.0009393708 0.02922561 0.0005173032 ## 7 7 0.03160116 0.2241139 0.02422636 0.0009247879 0.02858110 0.0004891560 ## 8 8 0.03148146 0.2300943 0.02414098 0.0009244857 0.02881080 0.0004732991 ## 9 9 0.03148587 0.2299594 0.02416144 0.0009477416 0.02913802 0.0004982399 ## 10 10 0.03148711 0.2298547 0.02415440 0.0009739512 0.02987084 0.0005053064 ## 11 11 0.03148089 0.2301187 0.02416120 0.0009953110 0.02990456 0.0005364930 ## 12 12 0.03148470 0.2299522 0.02416349 0.0009990068 0.02944639 0.0005495697 ## 13 13 0.03145749 0.2311967 0.02414219 0.0009791909 0.02841144 0.0005384081 ## 14 14 0.03147437 0.2303786 0.02416961 0.0009806357 0.02822536 0.0005623535 ## 15 15 0.03146569 0.2307427 0.02417507 0.0009936339 0.02783595 0.0005714702 ## 16 16 0.03148991 0.2296581 0.02420039 0.0009779886 0.02712579 0.0005488794 ## 17 17 0.03150643 0.2289046 0.02421673 0.0009893667 0.02727567 0.0005628079 ## 18 18 0.03149150 0.2296509 0.02419585 0.0010119458 0.02777386 0.0005791125 ## 19 19 0.03149602 0.2294674 0.02421031 0.0010101346 0.02752942 0.0005716861 ## 20 20 0.03149150 0.2297889 0.02421325 0.0010355425 0.02848300 0.0006030018 ## 21 21 0.03149346 0.2297230 0.02421668 0.0010347906 0.02832849 0.0005992109 ## 22 22 0.03148985 0.2299577 0.02420545 0.0010317694 0.02816307 0.0005935233 ## 23 23 0.03150560 0.2291566 0.02421693 0.0010302122 0.02771093 0.0005975507 ## 24 24 0.03150123 0.2293981 0.02421464 0.0010382557 0.02814206 0.0006112747 ## 25 25 0.03150100 0.2293860 0.02422176 0.0010254312 0.02723912 0.0006009309 ## 26 26 0.03149183 0.2298245 0.02421489 0.0010347978 0.02786493 0.0006039257 ## 27 27 0.03150301 0.2293084 0.02421839 0.0010322024 0.02814775 0.0006183281 ## 28 28 0.03151177 0.2288883 0.02423062 0.0010376854 0.02836636 0.0006076962 ## 29 29 0.03152629 0.2282336 0.02424962 0.0010350366 0.02874914 0.0006113150 ## 30 30 0.03150462 0.2292796 0.02422666 0.0010333894 0.02884529 0.0006052159 ## 31 31 0.03152222 0.2285141 0.02422667 0.0010231788 0.02850773 0.0005901465 ## 32 32 0.03152166 0.2285409 0.02422637 0.0010202863 0.02803710 0.0005907502 ## 33 33 0.03152680 0.2283914 0.02423341 0.0010282465 0.02891453 0.0005996862 ## 34 34 0.03152165 0.2286289 0.02422029 0.0010272815 0.02899737 0.0005787631 ## 35 35 0.03152216 0.2286122 0.02421592 0.0010333533 0.03000693 0.0005948846 ## 36 36 0.03151619 0.2289292 0.02420485 0.0010524680 0.03062424 0.0006020601 ## 37 37 0.03153723 0.2280375 0.02421334 0.0010653592 0.03092351 0.0006154587 ## 38 38 0.03153305 0.2282179 0.02421116 0.0010638597 0.03138850 0.0006098035 ## 39 39 0.03154750 0.2275818 0.02422317 0.0010763512 0.03139309 0.0006081373 ## 40 40 0.03155781 0.2271261 0.02423390 0.0010932059 0.03186254 0.0006352395 ## 41 41 0.03157039 0.2265291 0.02424142 0.0010873072 0.03168376 0.0006294560 ## 42 42 0.03158852 0.2257109 0.02425656 0.0010930039 0.03180567 0.0006343242 ## 43 43 0.03158944 0.2256653 0.02425314 0.0010937785 0.03161029 0.0006234741 ## 44 44 0.03161430 0.2245175 0.02427365 0.0010905645 0.03114733 0.0006186374 ## 45 45 0.03162132 0.2242148 0.02427171 0.0011006900 0.03111844 0.0006205233 ## 46 46 0.03163449 0.2236242 0.02427997 0.0010925258 0.03107534 0.0006140710 ## 47 47 0.03166233 0.2223907 0.02430563 0.0010785909 0.03055982 0.0006076598 ## 48 48 0.03167535 0.2218009 0.02432416 0.0010819878 0.03071511 0.0006062742 ## 49 49 0.03168743 0.2212780 0.02433099 0.0010958227 0.03117002 0.0006127448 ## 50 50 0.03169790 0.2208193 0.02433761 0.0011007041 0.03143607 0.0006122051 ## 51 51 0.03170385 0.2205859 0.02434684 0.0011148054 0.03176271 0.0006221330 ## 52 52 0.03171206 0.2202321 0.02435358 0.0011174232 0.03201158 0.0006302951 ## 53 53 0.03171275 0.2202419 0.02434438 0.0011190832 0.03228068 0.0006214280 ## 54 54 0.03171942 0.2199857 0.02434491 0.0011195699 0.03200830 0.0006272990 ## 55 55 0.03175177 0.2185689 0.02437405 0.0011249799 0.03205779 0.0006227720 ## 56 56 0.03176537 0.2179661 0.02439238 0.0011324860 0.03260363 0.0006260234 ## 57 57 0.03177822 0.2174000 0.02440121 0.0011261809 0.03236530 0.0006288714 ## 58 58 0.03178045 0.2172998 0.02440080 0.0011162237 0.03203053 0.0006184818 ## 59 59 0.03179325 0.2167466 0.02441368 0.0011150198 0.03146522 0.0006189895 ## 60 60 0.03180388 0.2162887 0.02442668 0.0011220389 0.03164539 0.0006329970 ## 61 61 0.03181178 0.2159335 0.02444023 0.0011229509 0.03175014 0.0006380280 ## 62 62 0.03182960 0.2151122 0.02445188 0.0011089964 0.03143470 0.0006256259 ## 63 63 0.03183547 0.2148748 0.02445908 0.0010986048 0.03100102 0.0006155681 ## 64 64 0.03183843 0.2148068 0.02446634 0.0010977924 0.03068568 0.0006170278 ## 65 65 0.03183741 0.2148634 0.02447038 0.0010925323 0.03044880 0.0006079075 ## 66 66 0.03184972 0.2143235 0.02447909 0.0010950967 0.03051703 0.0006122068 ## 67 67 0.03185145 0.2142726 0.02447925 0.0010948184 0.03048138 0.0006139235 ## 68 68 0.03186226 0.2138494 0.02448803 0.0011039317 0.03066073 0.0006143266 ## 69 69 0.03185310 0.2142871 0.02447907 0.0011164624 0.03095158 0.0006225425 ## 70 70 0.03184253 0.2147749 0.02447324 0.0011100205 0.03066794 0.0006184337 ## 71 71 0.03183982 0.2148468 0.02448019 0.0011046857 0.03037938 0.0006172816 ## 72 72 0.03183951 0.2149365 0.02448457 0.0011123471 0.03114095 0.0006249679 ## 73 73 0.03186126 0.2140233 0.02451008 0.0011240563 0.03150107 0.0006356698 ## 74 74 0.03187077 0.2136788 0.02452242 0.0011336733 0.03187902 0.0006445357 ## 75 75 0.03187397 0.2135744 0.02452600 0.0011269899 0.03173941 0.0006321105 ## 76 76 0.03189134 0.2128197 0.02453792 0.0011312457 0.03155818 0.0006380670 ## 77 77 0.03189578 0.2126348 0.02453994 0.0011233291 0.03111585 0.0006293408 ## 78 78 0.03189367 0.2127511 0.02453910 0.0011326136 0.03134337 0.0006401240 ## 79 79 0.03188700 0.2130560 0.02452915 0.0011322009 0.03117663 0.0006368514 ## 80 80 0.03189215 0.2128610 0.02453203 0.0011315557 0.03109205 0.0006370118 ## 81 81 0.03189711 0.2126117 0.02453410 0.0011220610 0.03106260 0.0006308790 ## 82 82 0.03190666 0.2122045 0.02453909 0.0011203534 0.03080748 0.0006359173 ## 83 83 0.03191382 0.2119136 0.02453932 0.0011280569 0.03099348 0.0006350279 ## 84 84 0.03192120 0.2116056 0.02454643 0.0011330155 0.03109308 0.0006403650 ## 85 85 0.03192608 0.2113545 0.02455771 0.0011206555 0.03036942 0.0006322890 ## 86 86 0.03193713 0.2108934 0.02456953 0.0011147236 0.03040124 0.0006246585 ## 87 87 0.03194515 0.2105549 0.02457501 0.0011184704 0.03029334 0.0006331645 ## 88 88 0.03195161 0.2103293 0.02457984 0.0011177850 0.03034283 0.0006389102 ## 89 89 0.03195398 0.2102553 0.02458073 0.0011276316 0.03057172 0.0006431748 ## 90 90 0.03195710 0.2101202 0.02457268 0.0011301721 0.03057785 0.0006517665 ## 91 91 0.03196854 0.2097160 0.02457845 0.0011418368 0.03117163 0.0006531160 ## 92 92 0.03197633 0.2094152 0.02458434 0.0011383684 0.03120996 0.0006534548 ## 93 93 0.03197903 0.2093464 0.02458929 0.0011361956 0.03103082 0.0006558597 ## 94 94 0.03198123 0.2093176 0.02459254 0.0011381135 0.03107207 0.0006574648 ## 95 95 0.03198888 0.2089592 0.02460281 0.0011353908 0.03115380 0.0006575974 ## 96 96 0.03198110 0.2092615 0.02459781 0.0011322933 0.03116535 0.0006618244 ## 97 97 0.03198395 0.2091719 0.02459428 0.0011320889 0.03132325 0.0006636691 ## 98 98 0.03199242 0.2089000 0.02459594 0.0011412590 0.03184657 0.0006708533 ## 99 99 0.03200024 0.2085274 0.02459575 0.0011408585 0.03154063 0.0006685708 ## 100 100 0.03199579 0.2087076 0.02459364 0.0011424166 0.03163829 0.0006779534 ## 101 101 0.03200704 0.2082228 0.02460036 0.0011467174 0.03177522 0.0006797074 ## 102 102 0.03200882 0.2081417 0.02460712 0.0011403892 0.03159193 0.0006778734 ## 103 103 0.03200486 0.2083381 0.02460558 0.0011407146 0.03166114 0.0006801245 ## 104 104 0.03200627 0.2082858 0.02460077 0.0011373283 0.03146443 0.0006756929 ## 105 105 0.03200221 0.2084937 0.02459636 0.0011439204 0.03170653 0.0006880109 ## 106 106 0.03201272 0.2080742 0.02460015 0.0011419743 0.03152758 0.0006905733 ## 107 107 0.03202531 0.2075159 0.02460630 0.0011352241 0.03137877 0.0006850509 ## 108 108 0.03202664 0.2074637 0.02460652 0.0011338225 0.03147074 0.0006869862 ## 109 109 0.03203332 0.2072115 0.02460458 0.0011374076 0.03165383 0.0006918002 ## 110 110 0.03202907 0.2073875 0.02460349 0.0011383616 0.03164868 0.0006920873 ## 111 111 0.03203395 0.2071944 0.02460799 0.0011406706 0.03171485 0.0006866740 ## 112 112 0.03203251 0.2072707 0.02461149 0.0011508964 0.03201357 0.0006954180 ## 113 113 0.03203444 0.2071493 0.02461243 0.0011475021 0.03174520 0.0006915712 ## 114 114 0.03204342 0.2067747 0.02462032 0.0011448259 0.03159749 0.0006918321 ## 115 115 0.03204435 0.2067141 0.02462258 0.0011416225 0.03153306 0.0006871036 ## 116 116 0.03204664 0.2066266 0.02462444 0.0011480858 0.03174972 0.0006872334 ## 117 117 0.03204745 0.2066152 0.02462266 0.0011451079 0.03163609 0.0006845313 ## 118 118 0.03204978 0.2065293 0.02462060 0.0011394005 0.03150090 0.0006782393 ## 119 119 0.03205151 0.2064905 0.02462147 0.0011443967 0.03167850 0.0006828976 ## 120 120 0.03205198 0.2064815 0.02461950 0.0011463997 0.03189578 0.0006843878 ## 121 121 0.03205210 0.2064996 0.02462163 0.0011453276 0.03211526 0.0006824211 ## 122 122 0.03205611 0.2063466 0.02462506 0.0011534222 0.03235874 0.0006822606 ## 123 123 0.03205325 0.2064445 0.02462534 0.0011473596 0.03202229 0.0006794365 ## 124 124 0.03205213 0.2065006 0.02462893 0.0011440842 0.03184795 0.0006762735 ## 125 125 0.03204809 0.2066764 0.02462606 0.0011399843 0.03153441 0.0006741584 ## 126 126 0.03204615 0.2067729 0.02462117 0.0011390618 0.03141533 0.0006768886 ## 127 127 0.03205351 0.2064814 0.02463005 0.0011355616 0.03140888 0.0006751462 ## 128 128 0.03206077 0.2061768 0.02463766 0.0011310169 0.03126794 0.0006684354 ## 129 129 0.03205975 0.2062339 0.02463285 0.0011337315 0.03130693 0.0006650687 ## 130 130 0.03205876 0.2062931 0.02463144 0.0011323441 0.03118920 0.0006613050 ## 131 131 0.03206160 0.2061909 0.02463509 0.0011285443 0.03101012 0.0006560125 ## 132 132 0.03206107 0.2062135 0.02463441 0.0011264702 0.03112544 0.0006540343 ## 133 133 0.03206577 0.2060358 0.02463949 0.0011257133 0.03099645 0.0006527849 ## 134 134 0.03207364 0.2057143 0.02464480 0.0011215810 0.03089706 0.0006508847 ## 135 135 0.03207002 0.2058688 0.02464425 0.0011213621 0.03096088 0.0006566557 ## 136 136 0.03207097 0.2058173 0.02464606 0.0011186111 0.03072206 0.0006521422 ## 137 137 0.03206766 0.2059567 0.02464149 0.0011139211 0.03054318 0.0006531895 ## 138 138 0.03206930 0.2058871 0.02464457 0.0011127252 0.03039835 0.0006506721 ## 139 139 0.03207310 0.2057303 0.02465217 0.0011137675 0.03045836 0.0006482800 ## 140 140 0.03207451 0.2056536 0.02465237 0.0011080715 0.03026135 0.0006441299 ## 141 141 0.03207719 0.2055463 0.02465513 0.0011095077 0.03026730 0.0006435190 ## 142 142 0.03207928 0.2054637 0.02465479 0.0011038163 0.03005955 0.0006413164 ## 143 143 0.03208103 0.2053896 0.02465744 0.0011019072 0.02996832 0.0006406203 ## 144 144 0.03208111 0.2053790 0.02465736 0.0010973384 0.02961049 0.0006345386 ## 145 145 0.03208194 0.2053612 0.02465545 0.0011018680 0.02974609 0.0006388692 ## 146 146 0.03208437 0.2052299 0.02465873 0.0010938023 0.02949692 0.0006338057 ## 147 147 0.03208406 0.2052562 0.02465668 0.0010935095 0.02956237 0.0006310461 ## 148 148 0.03208604 0.2051453 0.02465823 0.0010870176 0.02938592 0.0006249872 ## 149 149 0.03208693 0.2051206 0.02465492 0.0010869686 0.02945992 0.0006242159 ## 150 150 0.03208646 0.2051545 0.02465684 0.0010906012 0.02968915 0.0006307926 ## 151 151 0.03208991 0.2049983 0.02466033 0.0010850405 0.02962800 0.0006262904 ## 152 152 0.03208807 0.2050684 0.02465879 0.0010848320 0.02958173 0.0006266656 ## 153 153 0.03209198 0.2049048 0.02466160 0.0010865326 0.02967302 0.0006340689 ## 154 154 0.03209059 0.2049665 0.02466005 0.0010912670 0.02995850 0.0006370435 ## 155 155 0.03209271 0.2048634 0.02466185 0.0010852424 0.02969162 0.0006332863 ## 156 156 0.03208815 0.2050888 0.02465902 0.0010924470 0.02997242 0.0006412033 ## 157 157 0.03208726 0.2051485 0.02465890 0.0010906533 0.02999603 0.0006367577 ## 158 158 0.03208807 0.2051117 0.02466068 0.0010895200 0.02997214 0.0006380193 ## 159 159 0.03208713 0.2051510 0.02466076 0.0010950074 0.03011695 0.0006430644 ## 160 160 0.03208550 0.2052221 0.02465649 0.0010971070 0.03019039 0.0006400439 ## 161 161 0.03208434 0.2052808 0.02465471 0.0010984559 0.03027519 0.0006381159 ## 162 162 0.03208650 0.2051937 0.02465717 0.0010976655 0.03020050 0.0006388805 ## 163 163 0.03208480 0.2052655 0.02465666 0.0010968614 0.03018698 0.0006381939 ## 164 164 0.03208664 0.2051799 0.02465571 0.0010979172 0.03014250 0.0006396657 ## 165 165 0.03208534 0.2052296 0.02465249 0.0010947095 0.03006130 0.0006375254 ## 166 166 0.03208729 0.2051538 0.02465198 0.0010957634 0.03002880 0.0006368879 ## 167 167 0.03208545 0.2052294 0.02464769 0.0010957616 0.03001456 0.0006378650 ## 168 168 0.03208686 0.2051560 0.02464786 0.0010961027 0.02993675 0.0006418943 ## 169 169 0.03208900 0.2050673 0.02465059 0.0010945804 0.02986548 0.0006445203 ## 170 170 0.03209100 0.2049806 0.02465291 0.0010952796 0.02982943 0.0006436645 ## 171 171 0.03209308 0.2048980 0.02465493 0.0010934558 0.02983813 0.0006419822 ## 172 172 0.03208971 0.2050415 0.02465281 0.0010959212 0.02994237 0.0006448324 ## 173 173 0.03208690 0.2051598 0.02464906 0.0010990414 0.03000044 0.0006467680 ## 174 174 0.03208574 0.2052060 0.02464758 0.0010960653 0.02988539 0.0006440678 ## 175 175 0.03208904 0.2050636 0.02464807 0.0010936824 0.02987995 0.0006432163 ## 176 176 0.03209221 0.2049495 0.02465047 0.0010981691 0.03006503 0.0006459725 ## 177 177 0.03209210 0.2049623 0.02465121 0.0011015898 0.03018727 0.0006496947 ## 178 178 0.03209387 0.2048928 0.02465288 0.0011043859 0.03034912 0.0006483820 ## 179 179 0.03209545 0.2048292 0.02465458 0.0011027677 0.03035071 0.0006473268 ## 180 180 0.03209864 0.2047138 0.02465788 0.0011012264 0.03034704 0.0006475026 ## 181 181 0.03209769 0.2047604 0.02465674 0.0011031500 0.03050982 0.0006471425 ## 182 182 0.03210209 0.2045756 0.02466151 0.0011050947 0.03054713 0.0006483915 ## 183 183 0.03210369 0.2045122 0.02466073 0.0011021377 0.03041440 0.0006435666 ## 184 184 0.03210651 0.2043894 0.02466254 0.0011052458 0.03051528 0.0006463747 ## 185 185 0.03210607 0.2044233 0.02466032 0.0011044674 0.03045134 0.0006454267 ## 186 186 0.03210514 0.2044533 0.02465868 0.0011046857 0.03050533 0.0006450899 ## 187 187 0.03210623 0.2044012 0.02465785 0.0011019948 0.03032322 0.0006426781 ## 188 188 0.03210596 0.2044166 0.02465905 0.0011021026 0.03025874 0.0006438049 ## 189 189 0.03210699 0.2043724 0.02466068 0.0011042746 0.03029489 0.0006440600 ## 190 190 0.03210737 0.2043579 0.02466382 0.0011020023 0.03023518 0.0006424142 ## 191 191 0.03210572 0.2044321 0.02466306 0.0011056422 0.03038783 0.0006429226 ## 192 192 0.03210889 0.2042929 0.02466381 0.0011051824 0.03039140 0.0006419025 ## 193 193 0.03210620 0.2044115 0.02466275 0.0011069860 0.03042055 0.0006446823 ## 194 194 0.03210639 0.2044071 0.02466310 0.0011043911 0.03039051 0.0006425709 ## 195 195 0.03210837 0.2043225 0.02466366 0.0011032147 0.03033253 0.0006405611 ## 196 196 0.03210908 0.2042832 0.02466350 0.0011021880 0.03026979 0.0006390210 ## 197 197 0.03211204 0.2041602 0.02466543 0.0011028568 0.03025483 0.0006389382 ## 198 198 0.03211177 0.2041733 0.02466593 0.0011045549 0.03031012 0.0006391914 ## 199 199 0.03211207 0.2041501 0.02466657 0.0011028756 0.03021979 0.0006397886 ## 200 200 0.03211105 0.2041910 0.02466688 0.0011032678 0.03021656 0.0006398686 ## 201 201 0.03211192 0.2041520 0.02466683 0.0011034949 0.03022254 0.0006383202 ## 202 202 0.03211073 0.2042074 0.02466744 0.0011031915 0.03020890 0.0006384131 ## 203 203 0.03211102 0.2041871 0.02466820 0.0011034352 0.03016556 0.0006388333 ## 204 204 0.03210934 0.2042607 0.02466730 0.0011038130 0.03020391 0.0006372284 ## 205 205 0.03210879 0.2042884 0.02466635 0.0011043812 0.03021556 0.0006385534 ## 206 206 0.03210963 0.2042546 0.02466720 0.0011042217 0.03017080 0.0006389351 ## 207 207 0.03210741 0.2043499 0.02466485 0.0011037773 0.03018185 0.0006391489 ## 208 208 0.03210681 0.2043787 0.02466397 0.0011051015 0.03023139 0.0006404778 ## 209 209 0.03210924 0.2042686 0.02466627 0.0011054587 0.03023173 0.0006415652 ## 210 210 0.03210940 0.2042757 0.02466676 0.0011074000 0.03032859 0.0006436772 ## 211 211 0.03210883 0.2042997 0.02466565 0.0011078063 0.03033795 0.0006444732 ## 212 212 0.03210966 0.2042697 0.02466680 0.0011076091 0.03033941 0.0006453087 ## 213 213 0.03210924 0.2042822 0.02466630 0.0011072704 0.03033843 0.0006456218 ## 214 214 0.03210866 0.2043080 0.02466545 0.0011073205 0.03030701 0.0006458381 ## 215 215 0.03210968 0.2042603 0.02466500 0.0011077043 0.03029705 0.0006460638 ## 216 216 0.03211078 0.2042151 0.02466665 0.0011067384 0.03026335 0.0006449334 ## 217 217 0.03211109 0.2042072 0.02466717 0.0011092032 0.03036328 0.0006470520 ## 218 218 0.03211111 0.2042070 0.02466656 0.0011089075 0.03033337 0.0006467482 ## 219 219 0.03211051 0.2042295 0.02466618 0.0011083204 0.03031500 0.0006466827 ## 220 220 0.03211076 0.2042154 0.02466654 0.0011077153 0.03028606 0.0006450397 ## 221 221 0.03211001 0.2042474 0.02466652 0.0011080025 0.03032290 0.0006449498 ## 222 222 0.03211061 0.2042185 0.02466710 0.0011079167 0.03033603 0.0006443065 ## 223 223 0.03210934 0.2042676 0.02466648 0.0011072420 0.03030709 0.0006433694 ## 224 224 0.03211009 0.2042370 0.02466770 0.0011072195 0.03032682 0.0006431438 ## 225 225 0.03210996 0.2042470 0.02466728 0.0011070552 0.03031321 0.0006424427 ## 226 226 0.03210957 0.2042651 0.02466715 0.0011077269 0.03033567 0.0006430903 ## 227 227 0.03210969 0.2042642 0.02466744 0.0011083432 0.03038858 0.0006432803 ## 228 228 0.03210966 0.2042649 0.02466702 0.0011083884 0.03039151 0.0006432022 ## 229 229 0.03210980 0.2042614 0.02466716 0.0011091508 0.03042010 0.0006439305 ## 230 230 0.03210965 0.2042683 0.02466755 0.0011094279 0.03042562 0.0006438716 ## 231 231 0.03210959 0.2042718 0.02466768 0.0011091845 0.03042081 0.0006433408 ## 232 232 0.03211034 0.2042399 0.02466868 0.0011088124 0.03040087 0.0006427493 ## 233 233 0.03211031 0.2042421 0.02466841 0.0011094963 0.03043202 0.0006434366 ## 234 234 0.03211014 0.2042491 0.02466836 0.0011092755 0.03042107 0.0006430091 ## 235 235 0.03211022 0.2042449 0.02466844 0.0011091303 0.03041803 0.0006434017 ## 236 236 0.03210982 0.2042631 0.02466832 0.0011092561 0.03042793 0.0006437501 ## 237 237 0.03210997 0.2042566 0.02466848 0.0011088841 0.03040869 0.0006432413 ## 238 238 0.03210991 0.2042592 0.02466824 0.0011087237 0.03040023 0.0006431995 ## 239 239 0.03210989 0.2042603 0.02466821 0.0011087423 0.03039855 0.0006432065 ## 240 240 0.03210993 0.2042585 0.02466824 0.0011087027 0.03039707 0.0006431900 ## [1] "Best Model" ## nvmax ## 13 13

## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

## [1] "Coefficients of final model:"
##                  Estimate         2.5 %        97.5 %
## (Intercept)  1.972681e+00  1.956867e+00  1.988495e+00
## x4          -4.607173e-05 -6.334938e-05 -2.879408e-05
## x7           1.080812e-02  9.583611e-03  1.203263e-02
## x8           4.784756e-04  1.929724e-04  7.639787e-04
## x9           3.106132e-03  2.470605e-03  3.741659e-03
## x10          1.140634e-03  5.481000e-04  1.733168e-03
## x11          2.032330e+05  6.180148e+04  3.446645e+05
## x16          1.063749e-03  6.532151e-04  1.474284e-03
## x17          1.860411e-03  1.237166e-03  2.483656e-03
## stat14      -7.371136e-04 -1.207823e-03 -2.664039e-04
## stat41      -7.435917e-04 -1.216279e-03 -2.709043e-04
## stat98       3.577314e-03  3.108078e-03  4.046550e-03
## stat110     -3.392311e-03 -3.868431e-03 -2.916191e-03
## x18.sqrt     2.586108e-02  2.405283e-02  2.766932e-02

>>>>>>> 8e6f61bca4894b586983e20a3e14b1b8a049b903

Test

if (algo.backward.caret == TRUE){
  test.model(model.backward, data.test
             ,method = 'leapBackward',subopt = NULL
             ,formula = formula, feature.names = feature.names, label.names = label.names
             ,id = id
             ,draw.limits = TRUE, transformation = t)
}

## [1] "Summary of predicted values: "
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
<<<<<<< HEAD
##   2.044   2.084   2.097   2.097   2.109   2.147 
## [1] "leapBackward  Test MSE: 0.000942359887602509"

======= ## 2.039 2.084 2.097 2.097 2.109 2.145 ## [1] "leapBackward Test MSE: 0.00104530808325543"

>>>>>>> 8e6f61bca4894b586983e20a3e14b1b8a049b903

Stepwise Selection with CV

Train

if (algo.stepwise.caret == TRUE){
  set.seed(1)
  returned = train.caret.glmselect(formula = formula
                                   ,data =  data.train
                                   ,method = "leapSeq"
                                   ,feature.names = feature.names)
  model.stepwise = returned$model
  id = returned$id
}

## Aggregating results
## Selecting tuning parameters
## Fitting nvmax = 11 on full training set
## [1] "All models results"
##     nvmax       RMSE  Rsquared        MAE       RMSESD RsquaredSD        MAESD
## 1       1 0.03389262 0.1107374 0.02638098 0.0006522431 0.01843699 0.0004657941
## 2       2 0.03307022 0.1535661 0.02570143 0.0007777253 0.02125833 0.0006093741
## 3       3 0.03251205 0.1824264 0.02515777 0.0007730663 0.02790904 0.0005946623
## 4       4 0.03203058 0.2063268 0.02453996 0.0007618678 0.02742323 0.0006125272
## 5       5 0.03175409 0.2198443 0.02433833 0.0007521550 0.02365268 0.0005893048
## 6       6 0.03164410 0.2252731 0.02426658 0.0007067374 0.02069752 0.0005718563
## 7       7 0.03167451 0.2237877 0.02430027 0.0007134016 0.02161979 0.0006044690
## 8       8 0.03162055 0.2265125 0.02428486 0.0007295711 0.02287693 0.0005987685
## 9       9 0.03155615 0.2297157 0.02422169 0.0007806923 0.02479613 0.0006297838
## 10     10 0.03155548 0.2298092 0.02421996 0.0007214398 0.02383271 0.0005854693
## 11     11 0.03154196 0.2304901 0.02420858 0.0007129736 0.02369648 0.0005638611
## 12     12 0.03157136 0.2290734 0.02422468 0.0007175387 0.02209994 0.0005662709
## 13     13 0.03157326 0.2289631 0.02424003 0.0006890899 0.02081163 0.0005325302
## 14     14 0.03157408 0.2288482 0.02424375 0.0006872834 0.02012904 0.0005257180
## 15     15 0.03157894 0.2287061 0.02423653 0.0007038994 0.02024370 0.0005411458
## 16     16 0.03190636 0.2117547 0.02452156 0.0013404932 0.06017317 0.0011044116
## 17     17 0.03157406 0.2290131 0.02421312 0.0007224985 0.01997446 0.0005265877
## 18     18 0.03156651 0.2293337 0.02420193 0.0007170687 0.01830741 0.0005263061
## 19     19 0.03154426 0.2304284 0.02418362 0.0007083238 0.01837859 0.0005279866
## 20     20 0.03156336 0.2295238 0.02420827 0.0007248759 0.01924171 0.0005474819
## 21     21 0.03159715 0.2279797 0.02422729 0.0007282979 0.02017570 0.0005567951
## 22     22 0.03196738 0.2092553 0.02453578 0.0015485656 0.06013615 0.0012713111
## 23     23 0.03158918 0.2284546 0.02422965 0.0007397660 0.02140798 0.0005825951
## 24     24 0.03156738 0.2294569 0.02421477 0.0007204914 0.02062076 0.0005591127
## 25     25 0.03158046 0.2288811 0.02424395 0.0007370698 0.01940678 0.0005602539
## 26     26 0.03155988 0.2299272 0.02423487 0.0007381787 0.01977053 0.0005594708
## 27     27 0.03157513 0.2292237 0.02425307 0.0007616370 0.02089499 0.0005961089
## 28     28 0.03157278 0.2293200 0.02425732 0.0007545404 0.02083975 0.0005969809
## 29     29 0.03180893 0.2174105 0.02442729 0.0012809581 0.04991480 0.0009363540
## 30     30 0.03229356 0.1930513 0.02484382 0.0016910689 0.06879877 0.0013931207
## 31     31 0.03193126 0.2113926 0.02452373 0.0013507778 0.06042039 0.0010222070
## 32     32 0.03194276 0.2105584 0.02458709 0.0013168990 0.05826289 0.0010729542
## 33     33 0.03163171 0.2269222 0.02431474 0.0007451232 0.02212524 0.0005848146
## 34     34 0.03165120 0.2260814 0.02433254 0.0007545036 0.02282494 0.0005976554
## 35     35 0.03164835 0.2261771 0.02432278 0.0007779652 0.02291525 0.0006327695
## 36     36 0.03190482 0.2120608 0.02454376 0.0008175801 0.05080420 0.0008048053
## 37     37 0.03223647 0.1951826 0.02486195 0.0014064694 0.07066364 0.0011396934
## 38     38 0.03170411 0.2236700 0.02438520 0.0007675873 0.02116256 0.0006103664
## 39     39 0.03196900 0.2094742 0.02463244 0.0010131088 0.05118741 0.0008450926
## 40     40 0.03196216 0.2104704 0.02457026 0.0009346952 0.04384750 0.0007947740
## 41     41 0.03192549 0.2124119 0.02451896 0.0012361352 0.04679187 0.0009139803
## 42     42 0.03217811 0.2002617 0.02475941 0.0013738197 0.05953275 0.0010045000
## 43     43 0.03205242 0.2061287 0.02462206 0.0013589357 0.05964128 0.0010463279
## 44     44 0.03270386 0.1734083 0.02512338 0.0018333297 0.08130799 0.0013313729
## 45     45 0.03205640 0.2056472 0.02465931 0.0013004827 0.05601458 0.0010619360
## 46     46 0.03221936 0.1985616 0.02479355 0.0013553883 0.05856631 0.0009874377
## 47     47 0.03177494 0.2206460 0.02442074 0.0008064939 0.02222634 0.0006460526
## 48     48 0.03202344 0.2077207 0.02462188 0.0009752004 0.04581255 0.0008351891
## 49     49 0.03296207 0.1595841 0.02538980 0.0017383653 0.07823696 0.0013980231
## 50     50 0.03204341 0.2060375 0.02463894 0.0007839917 0.04815828 0.0007573110
## 51     51 0.03206358 0.2051349 0.02464930 0.0007638784 0.04789335 0.0007449423
## 52     52 0.03184275 0.2178206 0.02447732 0.0007952133 0.02297393 0.0006213095
## 53     53 0.03218564 0.2006009 0.02474453 0.0011034122 0.04444579 0.0008989274
## 54     54 0.03272897 0.1719717 0.02525041 0.0016035335 0.07328474 0.0012624810
## 55     55 0.03190696 0.2150266 0.02450950 0.0007919428 0.02295894 0.0006465792
## 56     56 0.03234443 0.1933654 0.02487484 0.0013027446 0.05620578 0.0009719069
## 57     57 0.03190826 0.2150342 0.02450711 0.0007731364 0.02170786 0.0006391728
## 58     58 0.03270840 0.1728509 0.02522079 0.0011853066 0.06469140 0.0010109080
## 59     59 0.03216460 0.2007868 0.02471767 0.0007355282 0.04601677 0.0007522352
## 60     60 0.03258182 0.1810157 0.02504379 0.0017598213 0.07367551 0.0014331603
## 61     61 0.03217749 0.2002409 0.02472311 0.0007516287 0.04654581 0.0007534026
## 62     62 0.03270112 0.1723941 0.02518733 0.0012381587 0.07342228 0.0010739223
## 63     63 0.03303636 0.1566573 0.02536752 0.0017599415 0.07813027 0.0014057263
## 64     64 0.03198178 0.2118771 0.02456126 0.0007936143 0.02250020 0.0006583984
## 65     65 0.03227865 0.1966534 0.02481696 0.0014181398 0.05569133 0.0011230864
## 66     66 0.03225265 0.1977175 0.02477948 0.0012661378 0.05455858 0.0009811456
## 67     67 0.03228552 0.1963687 0.02482691 0.0014201821 0.05564907 0.0011313731
## 68     68 0.03239186 0.1889456 0.02486805 0.0011488409 0.05940391 0.0009812912
## 69     69 0.03292106 0.1641962 0.02532547 0.0018663962 0.07439338 0.0015179714
## 70     70 0.03228190 0.1965133 0.02482179 0.0014066723 0.05535723 0.0011032126
## 71     71 0.03242249 0.1869698 0.02498789 0.0008577006 0.05900046 0.0008312052
## 72     72 0.03263117 0.1791488 0.02509048 0.0018208783 0.07199665 0.0014550252
## 73     73 0.03226859 0.1970791 0.02479467 0.0012548538 0.05441653 0.0009492339
## 74     74 0.03254785 0.1819450 0.02502171 0.0009745416 0.05587756 0.0009345276
## 75     75 0.03264442 0.1782365 0.02509928 0.0017374921 0.07186230 0.0014153600
## 76     76 0.03253261 0.1825747 0.02503149 0.0013337934 0.06604520 0.0011417823
## 77     77 0.03227804 0.1966769 0.02480360 0.0012537172 0.05433758 0.0009701228
## 78     78 0.03286111 0.1664006 0.02529508 0.0014125608 0.06860469 0.0011823598
## 79     79 0.03232460 0.1948419 0.02484955 0.0010716578 0.04348243 0.0008891385
## 80     80 0.03299645 0.1604910 0.02543018 0.0016574642 0.07354738 0.0012389834
## 81     81 0.03203145 0.2098580 0.02462138 0.0007695140 0.02243368 0.0006214841
## 82     82 0.03224029 0.1980646 0.02484341 0.0009336145 0.04602808 0.0007666668
## 83     83 0.03223523 0.1989800 0.02476874 0.0011971892 0.04715206 0.0009132621
## 84     84 0.03277294 0.1728990 0.02521700 0.0013303382 0.05919834 0.0009641456
## 85     85 0.03281866 0.1710558 0.02523939 0.0016711046 0.06877583 0.0012488075
## 86     86 0.03249750 0.1845183 0.02503379 0.0012801992 0.06427935 0.0010009530
## 87     87 0.03280002 0.1714870 0.02524755 0.0015214516 0.06847507 0.0011245466
## 88     88 0.03233594 0.1943903 0.02487820 0.0013793063 0.05447681 0.0010849318
## 89     89 0.03222450 0.1995041 0.02475916 0.0012002133 0.04772528 0.0009190266
## 90     90 0.03254352 0.1826926 0.02510358 0.0014340406 0.06510248 0.0011255931
## 91     91 0.03238513 0.1924834 0.02489125 0.0014818651 0.05697926 0.0011954186
## 92     92 0.03224006 0.1981625 0.02485293 0.0009259335 0.04623628 0.0007592645
## 93     93 0.03204973 0.2091133 0.02464788 0.0007630802 0.02266234 0.0006141097
## 94     94 0.03257437 0.1809023 0.02509379 0.0013011009 0.06567833 0.0011195969
## 95     95 0.03206123 0.2086692 0.02466295 0.0007724915 0.02299611 0.0006223798
## 96     96 0.03331895 0.1422237 0.02571213 0.0019243695 0.08460243 0.0015018316
## 97     97 0.03261531 0.1797927 0.02509662 0.0011951369 0.05910872 0.0010101957
## 98     98 0.03281894 0.1708758 0.02529712 0.0015227201 0.06837044 0.0011294593
## 99     99 0.03259488 0.1807404 0.02512520 0.0015255755 0.06668401 0.0012239505
## 100   100 0.03250003 0.1872431 0.02501616 0.0012202174 0.05246380 0.0008259194
## 101   101 0.03238220 0.1924862 0.02491359 0.0011120299 0.04670515 0.0009208317
## 102   102 0.03207302 0.2083361 0.02467570 0.0007658074 0.02330937 0.0006177188
## 103   103 0.03251042 0.1868173 0.02502162 0.0012198557 0.05247733 0.0008104407
## 104   104 0.03235978 0.1936575 0.02491642 0.0013618990 0.05396057 0.0010680689
## 105   105 0.03239992 0.1921270 0.02492509 0.0014720671 0.05693844 0.0011912118
## 106   106 0.03208365 0.2079157 0.02468668 0.0007690143 0.02360825 0.0006302179
## 107   107 0.03272777 0.1748933 0.02519339 0.0012914664 0.06361111 0.0009158302
## 108   108 0.03256879 0.1823655 0.02508556 0.0016432724 0.06728165 0.0012813883
## 109   109 0.03208839 0.2077815 0.02468660 0.0007638979 0.02321952 0.0006291254
## 110   110 0.03275143 0.1742155 0.02524319 0.0014720328 0.06578984 0.0012417361
## 111   111 0.03210022 0.2072567 0.02469912 0.0007532593 0.02329091 0.0006201568
## 112   112 0.03234495 0.1934208 0.02488906 0.0007455030 0.04916116 0.0007782915
## 113   113 0.03282220 0.1682226 0.02531206 0.0013679681 0.07386064 0.0011005833
## 114   114 0.03278215 0.1729357 0.02525850 0.0014818603 0.06615637 0.0012516033
## 115   115 0.03282348 0.1687880 0.02525418 0.0016128246 0.07653423 0.0012973311
## 116   116 0.03297523 0.1617093 0.02537799 0.0015938689 0.07732054 0.0013721641
## 117   117 0.03266643 0.1781347 0.02517356 0.0016298579 0.07095424 0.0013324249
## 118   118 0.03240974 0.1916885 0.02495676 0.0013292524 0.05280513 0.0010497223
## 119   119 0.03261332 0.1802813 0.02511146 0.0014298646 0.06552485 0.0011537237
## 120   120 0.03229448 0.1967973 0.02490154 0.0008657819 0.04189151 0.0007341068
## 121   121 0.03227531 0.1978130 0.02482283 0.0008834765 0.04170865 0.0007578720
## 122   122 0.03234726 0.1942724 0.02489595 0.0007634031 0.04729228 0.0007926131
## 123   123 0.03239991 0.1926545 0.02498390 0.0009662668 0.03903177 0.0009746519
## 124   124 0.03263165 0.1805597 0.02509780 0.0010689266 0.04606071 0.0007422657
## 125   125 0.03284427 0.1695182 0.02529752 0.0015538037 0.06662734 0.0013126628
## 126   126 0.03243223 0.1911956 0.02493885 0.0008845017 0.03451720 0.0005518075
## 127   127 0.03213794 0.2059163 0.02471882 0.0007563696 0.02446492 0.0006160069
## 128   128 0.03240114 0.1923913 0.02497495 0.0011193227 0.04702881 0.0009758222
## 129   129 0.03214064 0.2057934 0.02472525 0.0007576194 0.02471343 0.0006083244
## 130   130 0.03234329 0.1953112 0.02489857 0.0012666434 0.05064304 0.0010301210
## 131   131 0.03215423 0.2053147 0.02473458 0.0007625378 0.02500559 0.0006138360
## 132   132 0.03236292 0.1947478 0.02494170 0.0008428065 0.03130747 0.0007882416
## 133   133 0.03246571 0.1880965 0.02499406 0.0008095321 0.05050795 0.0007927231
## 134   134 0.03234827 0.1951122 0.02491964 0.0009961354 0.04021427 0.0008235674
## 135   135 0.03214651 0.2056296 0.02473753 0.0007550915 0.02504273 0.0006088901
## 136   136 0.03250483 0.1867763 0.02501774 0.0012122568 0.05062705 0.0009244021
## 137   137 0.03272336 0.1755202 0.02518225 0.0008100232 0.04594793 0.0006543020
## 138   138 0.03286597 0.1680172 0.02534444 0.0013508950 0.05540468 0.0011132573
## 139   139 0.03213980 0.2059246 0.02472159 0.0007383313 0.02408760 0.0006088668
## 140   140 0.03279876 0.1723497 0.02522430 0.0010439499 0.04878411 0.0008361220
## 141   141 0.03228084 0.1980190 0.02485333 0.0008434060 0.03881870 0.0006539497
## 142   142 0.03231800 0.1962194 0.02488409 0.0007288258 0.04264854 0.0007560841
## 143   143 0.03231249 0.1964752 0.02487780 0.0007265343 0.04253209 0.0007564128
## 144   144 0.03250434 0.1870728 0.02498109 0.0012564309 0.05271093 0.0010187274
## 145   145 0.03246186 0.1882370 0.02501522 0.0007800813 0.05030780 0.0007485211
## 146   146 0.03228614 0.1980761 0.02483963 0.0009421280 0.03782737 0.0007582706
## 147   147 0.03212439 0.2066283 0.02471155 0.0007572386 0.02475593 0.0006200199
## 148   148 0.03279512 0.1727491 0.02526594 0.0013497432 0.05228611 0.0011412622
## 149   149 0.03212233 0.2067047 0.02471583 0.0007487306 0.02448356 0.0006148482
## 150   150 0.03238229 0.1939010 0.02490365 0.0007968104 0.02864210 0.0004684423
## 151   151 0.03275673 0.1744202 0.02523422 0.0012607549 0.05258216 0.0010422328
## 152   152 0.03236674 0.1945862 0.02488977 0.0007960599 0.02826401 0.0004687335
## 153   153 0.03261601 0.1823983 0.02506313 0.0011971036 0.04331338 0.0008337506
## 154   154 0.03273379 0.1753356 0.02524099 0.0011649759 0.04947155 0.0010052775
## 155   155 0.03212747 0.2065048 0.02471961 0.0007451542 0.02409970 0.0006054221
## 156   156 0.03230235 0.1973791 0.02485826 0.0009664567 0.03912220 0.0007777554
## 157   157 0.03227549 0.1983409 0.02485214 0.0008436627 0.03881141 0.0006468913
## 158   158 0.03285877 0.1682981 0.02535308 0.0012703161 0.05658262 0.0011175112
## 159   159 0.03244966 0.1894975 0.02496935 0.0010867507 0.04703700 0.0008743687
## 160   160 0.03230124 0.1974384 0.02484859 0.0009581915 0.03913552 0.0007714527
## 161   161 0.03258283 0.1833713 0.02507221 0.0006930945 0.04231538 0.0005990178
## 162   162 0.03237783 0.1942782 0.02488930 0.0012257032 0.04492003 0.0009677082
## 163   163 0.03229270 0.1977343 0.02483510 0.0008638382 0.04052628 0.0007397562
## 164   164 0.03213083 0.2063660 0.02471082 0.0007154935 0.02319874 0.0005939863
## 165   165 0.03229131 0.1977951 0.02483823 0.0008661526 0.04053791 0.0007432873
## 166   166 0.03212787 0.2064684 0.02471457 0.0007220392 0.02311780 0.0005953232
## 167   167 0.03236467 0.1946424 0.02492524 0.0008838034 0.03421602 0.0008231460
## 168   168 0.03254317 0.1855407 0.02502903 0.0012894299 0.05395799 0.0010496752
## 169   169 0.03238119 0.1939853 0.02490309 0.0007779993 0.02780307 0.0004557753
## 170   170 0.03213389 0.2062221 0.02471898 0.0007266104 0.02328550 0.0005914244
## 171   171 0.03230372 0.1974000 0.02485292 0.0010141597 0.03631847 0.0007877086
## 172   172 0.03213171 0.2063021 0.02472116 0.0007275140 0.02313804 0.0005910438
## 173   173 0.03212436 0.2066456 0.02471346 0.0007305029 0.02332999 0.0005987271
## 174   174 0.03236115 0.1948452 0.02492836 0.0008823393 0.03377038 0.0008177006
## 175   175 0.03212588 0.2065730 0.02471868 0.0007287127 0.02345189 0.0005973729
## 176   176 0.03230320 0.1973545 0.02486245 0.0009675710 0.03941914 0.0007817729
## 177   177 0.03233930 0.1955725 0.02490764 0.0007389759 0.04430253 0.0007780034
## 178   178 0.03212460 0.2066435 0.02472257 0.0007308067 0.02353279 0.0005980228
## 179   179 0.03211966 0.2068668 0.02471943 0.0007344497 0.02365057 0.0005986615
## 180   180 0.03212345 0.2067046 0.02472209 0.0007317950 0.02354773 0.0005965431
## 181   181 0.03227059 0.1986670 0.02484626 0.0008333514 0.03838499 0.0006473446
## 182   182 0.03212549 0.2066035 0.02471853 0.0007340489 0.02363249 0.0006065225
## 183   183 0.03212182 0.2067590 0.02471665 0.0007372081 0.02365035 0.0006074755
## 184   184 0.03228411 0.1983258 0.02487134 0.0011314842 0.04350718 0.0009678256
## 185   185 0.03231140 0.1968470 0.02489048 0.0009759886 0.03877548 0.0008057550
## 186   186 0.03261688 0.1826699 0.02507366 0.0012117376 0.04338476 0.0008449042
## 187   187 0.03212354 0.2067003 0.02472043 0.0007349509 0.02385099 0.0006079329
## 188   188 0.03271750 0.1760710 0.02524236 0.0010796804 0.04977342 0.0009309751
## 189   189 0.03212454 0.2066545 0.02472041 0.0007402202 0.02392888 0.0006107112
## 190   190 0.03237661 0.1941804 0.02494091 0.0009262456 0.03585763 0.0008543306
## 191   191 0.03227252 0.1986018 0.02484862 0.0008484927 0.03888484 0.0006611327
## 192   192 0.03212279 0.2067393 0.02471832 0.0007429165 0.02397257 0.0006142717
## 193   193 0.03212049 0.2068400 0.02471873 0.0007441163 0.02400649 0.0006163243
## 194   194 0.03236386 0.1948409 0.02489572 0.0007700140 0.02684707 0.0004516523
## 195   195 0.03254624 0.1853773 0.02507973 0.0009996753 0.04662736 0.0009464343
## 196   196 0.03211866 0.2069436 0.02471517 0.0007440972 0.02388126 0.0006151766
## 197   197 0.03212030 0.2068781 0.02471536 0.0007446741 0.02398357 0.0006153619
## 198   198 0.03212070 0.2068622 0.02471730 0.0007420512 0.02392750 0.0006132222
## 199   199 0.03254132 0.1855151 0.02507159 0.0009709762 0.05386286 0.0009242990
## 200   200 0.03247202 0.1883849 0.02502590 0.0010534061 0.04898955 0.0008330219
## 201   201 0.03231617 0.1969197 0.02486917 0.0010106702 0.04147785 0.0008086191
## 202   202 0.03212045 0.2068743 0.02471308 0.0007398835 0.02397711 0.0006106790
## 203   203 0.03229894 0.1976979 0.02485596 0.0009101831 0.04240294 0.0007931080
## 204   204 0.03211407 0.2071354 0.02470865 0.0007444526 0.02399015 0.0006109085
## 205   205 0.03229148 0.1981582 0.02487531 0.0011880177 0.04578411 0.0010150249
## 206   206 0.03211671 0.2070267 0.02471071 0.0007447954 0.02393297 0.0006106550
## 207   207 0.03211887 0.2069371 0.02471254 0.0007427624 0.02402469 0.0006106533
## 208   208 0.03261720 0.1824213 0.02511071 0.0008691547 0.03283763 0.0006916846
## 209   209 0.03212021 0.2068822 0.02471515 0.0007409750 0.02398888 0.0006081807
## 210   210 0.03212055 0.2068709 0.02471569 0.0007407612 0.02400551 0.0006075216
## 211   211 0.03212133 0.2068386 0.02471700 0.0007418947 0.02403101 0.0006077557
## 212   212 0.03231318 0.1968899 0.02488291 0.0009903616 0.03938384 0.0008081808
## 213   213 0.03212086 0.2068608 0.02471562 0.0007435165 0.02402960 0.0006077945
## 214   214 0.03212133 0.2068388 0.02471609 0.0007441390 0.02405444 0.0006079927
## 215   215 0.03268063 0.1801816 0.02516311 0.0014002530 0.05227637 0.0011752653
## 216   216 0.03230009 0.1976550 0.02485208 0.0010396276 0.03742624 0.0008042829
## 217   217 0.03212368 0.2067302 0.02471694 0.0007412252 0.02386297 0.0006050774
## 218   218 0.03212379 0.2067215 0.02471769 0.0007408228 0.02386854 0.0006057193
## 219   219 0.03212279 0.2067716 0.02471636 0.0007421437 0.02393657 0.0006064402
## 220   220 0.03239850 0.1934103 0.02495784 0.0009593283 0.03735062 0.0008821692
## 221   221 0.03212575 0.2066443 0.02471894 0.0007413844 0.02395601 0.0006063551
## 222   222 0.03255048 0.1851097 0.02508822 0.0009753751 0.05303685 0.0009280365
## 223   223 0.03233454 0.1962169 0.02489273 0.0010401791 0.04259350 0.0008456203
## 224   224 0.03258596 0.1843012 0.02507020 0.0014725559 0.05340019 0.0011604255
## 225   225 0.03212529 0.2066575 0.02471795 0.0007423461 0.02394726 0.0006068688
## 226   226 0.03233024 0.1963998 0.02488963 0.0010301119 0.04208109 0.0008380879
## 227   227 0.03230123 0.1975935 0.02487127 0.0008882659 0.04111235 0.0006762506
## 228   228 0.03237485 0.1943663 0.02489854 0.0007866438 0.02791711 0.0004657703
## 229   229 0.03212581 0.2066407 0.02471867 0.0007424296 0.02396027 0.0006065668
## 230   230 0.03233011 0.1962688 0.02489453 0.0010210913 0.04062813 0.0008329102
## 231   231 0.03232256 0.1967568 0.02487605 0.0009375355 0.04385260 0.0008125199
## 232   232 0.03254075 0.1857811 0.02502507 0.0010065551 0.03596151 0.0006477208
## 233   233 0.03232399 0.1968593 0.02490264 0.0012425605 0.04796890 0.0010621841
## 234   234 0.03212530 0.2066589 0.02471809 0.0007407540 0.02389895 0.0006053082
## 235   235 0.03242393 0.1928416 0.02495409 0.0013546307 0.04903128 0.0011069195
## 236   236 0.03246543 0.1890727 0.02499402 0.0010984918 0.04737600 0.0008141455
## 237   237 0.03271168 0.1773100 0.02522445 0.0015345402 0.05998383 0.0012653944
## 238   238 0.03271903 0.1767379 0.02522470 0.0012565159 0.05810254 0.0009799755
## 239   239 0.03336489 0.1468546 0.02575478 0.0013820283 0.06609633 0.0013056925
## 240   240 0.03212568 0.2066400 0.02471817 0.0007406867 0.02389293 0.0006054287
## [1] "Best Model"
##    nvmax
## 11    11

## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

## [1] "Coefficients of final model:"
##                  Estimate         2.5 %        97.5 %
## (Intercept)  1.9943108240  1.987270e+00  2.001352e+00
## x4          -0.0000563195 -7.366668e-05 -3.897232e-05
## x7           0.0111695138  9.941573e-03  1.239745e-02
## x9           0.0032703436  2.633200e-03  3.907487e-03
## x10          0.0010757959  4.818071e-04  1.669785e-03
## x16          0.0009034675  4.932559e-04  1.313679e-03
## x17          0.0013944496  7.693954e-04  2.019504e-03
## x21          0.0001290356  4.794220e-05  2.101289e-04
## stat14      -0.0009237427 -1.396307e-03 -4.511779e-04
## stat98       0.0035049260  3.034519e-03  3.975332e-03
## stat110     -0.0031947718 -3.668557e-03 -2.720987e-03
## x18.sqrt     0.0265348474  2.470918e-02  2.836052e-02

Test

if (algo.stepwise.caret == TRUE){
  test.model(model.stepwise, data.test
             ,method = 'leapSeq',subopt = NULL
             ,formula = formula, feature.names = feature.names, label.names = label.names
             ,id = id
             ,draw.limits = TRUE, transformation = t)
  
}

## [1] "Summary of predicted values: "
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
<<<<<<< HEAD
##   2.033   2.085   2.097   2.097   2.109   2.151 
## [1] "leapSeq  Test MSE: 0.000918627674071896"

======= ## 2.037 2.084 2.097 2.097 2.109 2.144 ## [1] "leapSeq Test MSE: 0.00103220592496655"

>>>>>>> 8e6f61bca4894b586983e20a3e14b1b8a049b903

LASSO with CV

Train

if (algo.LASSO.caret == TRUE){
  set.seed(1)
  tune.grid= expand.grid(alpha = 1,lambda = 10^seq(from=-4,to=-2,length=100))
  returned = train.caret.glmselect(formula = formula
                                   ,data =  data.train
                                   ,method = "glmnet"
                                   ,subopt = 'LASSO'
                                   ,tune.grid = tune.grid
                                   ,feature.names = feature.names)
  model.LASSO.caret = returned$model
}

## Aggregating results
## Selecting tuning parameters
<<<<<<< HEAD
## Fitting alpha = 1, lambda = 0.000559 on full training set
=======
## Fitting alpha = 1, lambda = 0.000586 on full training set
>>>>>>> 8e6f61bca4894b586983e20a3e14b1b8a049b903
## glmnet 
## 
## 5584 samples
##  240 predictor
## 
## No pre-processing
## Resampling: Cross-Validated (10 fold) 
## Summary of sample sizes: 5026, 5026, 5026, 5025, 5025, 5026, ... 
## Resampling results across tuning parameters:
## 
##   lambda        RMSE        Rsquared   MAE       
<<<<<<< HEAD
##   0.0001000000  0.03228576  0.2064380  0.02476806
##   0.0001047616  0.03227771  0.2067390  0.02476232
##   0.0001097499  0.03226954  0.2070462  0.02475657
##   0.0001149757  0.03226119  0.2073622  0.02475076
##   0.0001204504  0.03225267  0.2076868  0.02474504
##   0.0001261857  0.03224387  0.2080246  0.02473914
##   0.0001321941  0.03223491  0.2083699  0.02473328
##   0.0001384886  0.03222580  0.2087234  0.02472756
##   0.0001450829  0.03221656  0.2090844  0.02472199
##   0.0001519911  0.03220742  0.2094424  0.02471646
##   0.0001592283  0.03219816  0.2098075  0.02471083
##   0.0001668101  0.03218869  0.2101859  0.02470498
##   0.0001747528  0.03217910  0.2105728  0.02469923
##   0.0001830738  0.03216926  0.2109742  0.02469306
##   0.0001917910  0.03215933  0.2113839  0.02468686
##   0.0002009233  0.03214933  0.2118013  0.02468058
##   0.0002104904  0.03213924  0.2122268  0.02467435
##   0.0002205131  0.03212904  0.2126618  0.02466789
##   0.0002310130  0.03211883  0.2131024  0.02466143
##   0.0002420128  0.03210841  0.2135598  0.02465457
##   0.0002535364  0.03209829  0.2140101  0.02464786
##   0.0002656088  0.03208856  0.2144518  0.02464084
##   0.0002782559  0.03207945  0.2148724  0.02463401
##   0.0002915053  0.03207058  0.2152909  0.02462730
##   0.0003053856  0.03206206  0.2157013  0.02462064
##   0.0003199267  0.03205339  0.2161297  0.02461439
##   0.0003351603  0.03204509  0.2165493  0.02460858
##   0.0003511192  0.03203737  0.2169497  0.02460353
##   0.0003678380  0.03203043  0.2173232  0.02459932
##   0.0003853529  0.03202361  0.2176976  0.02459580
##   0.0004037017  0.03201735  0.2180551  0.02459308
##   0.0004229243  0.03201211  0.2183732  0.02459115
##   0.0004430621  0.03200808  0.2186438  0.02458977
##   0.0004641589  0.03200456  0.2189003  0.02458951
##   0.0004862602  0.03200155  0.2191402  0.02459007
##   0.0005094138  0.03199948  0.2193436  0.02459184
##   0.0005336699  0.03199854  0.2195013  0.02459490
##   0.0005590810  0.03199832  0.2196341  0.02459877
##   0.0005857021  0.03199938  0.2197149  0.02460353
##   0.0006135907  0.03200055  0.2198031  0.02460804
##   0.0006428073  0.03200240  0.2198708  0.02461293
##   0.0006734151  0.03200492  0.2199173  0.02461764
##   0.0007054802  0.03200874  0.2199122  0.02462310
##   0.0007390722  0.03201346  0.2198770  0.02462914
##   0.0007742637  0.03201947  0.2197889  0.02463604
##   0.0008111308  0.03202592  0.2197064  0.02464268
##   0.0008497534  0.03203364  0.2195740  0.02465057
##   0.0008902151  0.03204343  0.2193511  0.02465944
##   0.0009326033  0.03205516  0.2190433  0.02466961
##   0.0009770100  0.03206837  0.2186811  0.02468145
##   0.0010235310  0.03208380  0.2182201  0.02469528
##   0.0010722672  0.03210033  0.2177294  0.02471028
##   0.0011233240  0.03211846  0.2171761  0.02472735
##   0.0011768120  0.03213470  0.2167630  0.02474330
##   0.0012328467  0.03215104  0.2163840  0.02475901
##   0.0012915497  0.03216667  0.2160860  0.02477452
##   0.0013530478  0.03218310  0.2157880  0.02479059
##   0.0014174742  0.03220140  0.2154357  0.02480948
##   0.0014849683  0.03222194  0.2150086  0.02483081
##   0.0015556761  0.03224445  0.2145226  0.02485464
##   0.0016297508  0.03226926  0.2139634  0.02488105
##   0.0017073526  0.03229652  0.2133225  0.02490917
##   0.0017886495  0.03232636  0.2125956  0.02493918
##   0.0018738174  0.03235829  0.2118186  0.02497095
##   0.0019630407  0.03239219  0.2110041  0.02500403
##   0.0020565123  0.03242568  0.2103095  0.02503698
##   0.0021544347  0.03246075  0.2096169  0.02507189
##   0.0022570197  0.03249606  0.2090355  0.02510712
##   0.0023644894  0.03253415  0.2084098  0.02514434
##   0.0024770764  0.03257588  0.2076910  0.02518442
##   0.0025950242  0.03262162  0.2068602  0.02522766
##   0.0027185882  0.03267174  0.2058957  0.02527416
##   0.0028480359  0.03272666  0.2047718  0.02532376
##   0.0029836472  0.03278684  0.2034570  0.02537698
##   0.0031257158  0.03285276  0.2019130  0.02543448
##   0.0032745492  0.03292496  0.2000921  0.02549745
##   0.0034304693  0.03300402  0.1979353  0.02556541
##   0.0035938137  0.03309058  0.1953695  0.02563875
##   0.0037649358  0.03318528  0.1923058  0.02571821
##   0.0039442061  0.03328586  0.1889009  0.02580270
##   0.0041320124  0.03339347  0.1850321  0.02589114
##   0.0043287613  0.03349602  0.1818112  0.02597489
##   0.0045348785  0.03360379  0.1783076  0.02606287
##   0.0047508102  0.03372085  0.1740859  0.02615709
##   0.0049770236  0.03384857  0.1688900  0.02625893
##   0.0052140083  0.03398754  0.1624760  0.02636955
##   0.0054622772  0.03413695  0.1547476  0.02648772
##   0.0057223677  0.03428323  0.1470087  0.02660214
##   0.0059948425  0.03443218  0.1385423  0.02671791
##   0.0062802914  0.03456278  0.1319602  0.02681402
##   0.0065793322  0.03469603  0.1247634  0.02690998
##   0.0068926121  0.03482128  0.1184698  0.02699800
##   0.0072208090  0.03495233  0.1109458  0.02709032
##   0.0075646333  0.03505674  0.1068584  0.02716450
##   0.0079248290  0.03515278  0.1042371  0.02723276
##   0.0083021757  0.03524229  0.1038025  0.02729509
##   0.0086974900  0.03533734  0.1038025  0.02736183
##   0.0091116276  0.03544136  0.1038025  0.02743474
##   0.0095454846  0.03555519  0.1038025  0.02751488
##   0.0100000000  0.03567970  0.1038025  0.02760324
## 
## Tuning parameter 'alpha' was held constant at a value of 1
## RMSE was used to select the optimal model using the smallest value.
## The final values used for the model were alpha = 1 and lambda = 0.000559081.

##    alpha      lambda
## 38     1 0.000559081
##     alpha       lambda       RMSE  Rsquared        MAE       RMSESD RsquaredSD        MAESD
## 1       1 0.0001000000 0.03228576 0.2064380 0.02476806 0.0008712829 0.03676116 0.0005768569
## 2       1 0.0001047616 0.03227771 0.2067390 0.02476232 0.0008708951 0.03685607 0.0005758343
## 3       1 0.0001097499 0.03226954 0.2070462 0.02475657 0.0008705209 0.03695773 0.0005748383
## 4       1 0.0001149757 0.03226119 0.2073622 0.02475076 0.0008702297 0.03706628 0.0005741082
## 5       1 0.0001204504 0.03225267 0.2076868 0.02474504 0.0008699447 0.03718157 0.0005734114
## 6       1 0.0001261857 0.03224387 0.2080246 0.02473914 0.0008695922 0.03730062 0.0005729025
## 7       1 0.0001321941 0.03223491 0.2083699 0.02473328 0.0008692183 0.03742283 0.0005725269
## 8       1 0.0001384886 0.03222580 0.2087234 0.02472756 0.0008687065 0.03754417 0.0005721548
## 9       1 0.0001450829 0.03221656 0.2090844 0.02472199 0.0008681960 0.03767055 0.0005720432
## 10      1 0.0001519911 0.03220742 0.2094424 0.02471646 0.0008679047 0.03779970 0.0005717913
## 11      1 0.0001592283 0.03219816 0.2098075 0.02471083 0.0008676298 0.03793179 0.0005714045
## 12      1 0.0001668101 0.03218869 0.2101859 0.02470498 0.0008673946 0.03807156 0.0005707816
## 13      1 0.0001747528 0.03217910 0.2105728 0.02469923 0.0008670571 0.03821218 0.0005698664
## 14      1 0.0001830738 0.03216926 0.2109742 0.02469306 0.0008666479 0.03835244 0.0005688149
## 15      1 0.0001917910 0.03215933 0.2113839 0.02468686 0.0008662711 0.03849779 0.0005677215
## 16      1 0.0002009233 0.03214933 0.2118013 0.02468058 0.0008661909 0.03864507 0.0005663444
## 17      1 0.0002104904 0.03213924 0.2122268 0.02467435 0.0008660061 0.03879461 0.0005648880
## 18      1 0.0002205131 0.03212904 0.2126618 0.02466789 0.0008656690 0.03893572 0.0005630387
## 19      1 0.0002310130 0.03211883 0.2131024 0.02466143 0.0008652569 0.03907659 0.0005609128
## 20      1 0.0002420128 0.03210841 0.2135598 0.02465457 0.0008643713 0.03922826 0.0005584429
## 21      1 0.0002535364 0.03209829 0.2140101 0.02464786 0.0008633423 0.03938504 0.0005559140
## 22      1 0.0002656088 0.03208856 0.2144518 0.02464084 0.0008620351 0.03956064 0.0005535882
## 23      1 0.0002782559 0.03207945 0.2148724 0.02463401 0.0008604190 0.03974433 0.0005512395
## 24      1 0.0002915053 0.03207058 0.2152909 0.02462730 0.0008585401 0.03991542 0.0005483817
## 25      1 0.0003053856 0.03206206 0.2157013 0.02462064 0.0008564390 0.04008625 0.0005451657
## 26      1 0.0003199267 0.03205339 0.2161297 0.02461439 0.0008540551 0.04025166 0.0005415283
## 27      1 0.0003351603 0.03204509 0.2165493 0.02460858 0.0008513204 0.04040255 0.0005378772
## 28      1 0.0003511192 0.03203737 0.2169497 0.02460353 0.0008484707 0.04055637 0.0005340412
## 29      1 0.0003678380 0.03203043 0.2173232 0.02459932 0.0008452682 0.04070167 0.0005296175
## 30      1 0.0003853529 0.03202361 0.2176976 0.02459580 0.0008414949 0.04080626 0.0005247790
## 31      1 0.0004037017 0.03201735 0.2180551 0.02459308 0.0008374052 0.04089338 0.0005195409
## 32      1 0.0004229243 0.03201211 0.2183732 0.02459115 0.0008327949 0.04097045 0.0005135050
## 33      1 0.0004430621 0.03200808 0.2186438 0.02458977 0.0008278291 0.04103836 0.0005072873
## 34      1 0.0004641589 0.03200456 0.2189003 0.02458951 0.0008227433 0.04107595 0.0005007692
## 35      1 0.0004862602 0.03200155 0.2191402 0.02459007 0.0008177335 0.04108651 0.0004934100
## 36      1 0.0005094138 0.03199948 0.2193436 0.02459184 0.0008129325 0.04105391 0.0004866174
## 37      1 0.0005336699 0.03199854 0.2195013 0.02459490 0.0008077224 0.04097500 0.0004794737
## 38      1 0.0005590810 0.03199832 0.2196341 0.02459877 0.0008023265 0.04087601 0.0004724684
## 39      1 0.0005857021 0.03199938 0.2197149 0.02460353 0.0007967162 0.04075587 0.0004656081
## 40      1 0.0006135907 0.03200055 0.2198031 0.02460804 0.0007912155 0.04062684 0.0004594653
## 41      1 0.0006428073 0.03200240 0.2198708 0.02461293 0.0007860947 0.04049816 0.0004532403
## 42      1 0.0006734151 0.03200492 0.2199173 0.02461764 0.0007816584 0.04039912 0.0004477080
## 43      1 0.0007054802 0.03200874 0.2199122 0.02462310 0.0007776225 0.04029783 0.0004429947
## 44      1 0.0007390722 0.03201346 0.2198770 0.02462914 0.0007747006 0.04019551 0.0004392131
## 45      1 0.0007742637 0.03201947 0.2197889 0.02463604 0.0007716284 0.04007150 0.0004358775
## 46      1 0.0008111308 0.03202592 0.2197064 0.02464268 0.0007685012 0.03997913 0.0004335174
## 47      1 0.0008497534 0.03203364 0.2195740 0.02465057 0.0007652464 0.03986630 0.0004313486
## 48      1 0.0008902151 0.03204343 0.2193511 0.02465944 0.0007610420 0.03967315 0.0004283191
## 49      1 0.0009326033 0.03205516 0.2190433 0.02466961 0.0007569148 0.03945970 0.0004252546
## 50      1 0.0009770100 0.03206837 0.2186811 0.02468145 0.0007528138 0.03929506 0.0004216231
## 51      1 0.0010235310 0.03208380 0.2182201 0.02469528 0.0007485090 0.03911976 0.0004179498
## 52      1 0.0010722672 0.03210033 0.2177294 0.02471028 0.0007436144 0.03895638 0.0004149421
## 53      1 0.0011233240 0.03211846 0.2171761 0.02472735 0.0007384787 0.03881892 0.0004121102
## 54      1 0.0011768120 0.03213470 0.2167630 0.02474330 0.0007320138 0.03868175 0.0004089346
## 55      1 0.0012328467 0.03215104 0.2163840 0.02475901 0.0007258335 0.03853015 0.0004060597
## 56      1 0.0012915497 0.03216667 0.2160860 0.02477452 0.0007198690 0.03844135 0.0004040509
## 57      1 0.0013530478 0.03218310 0.2157880 0.02479059 0.0007145899 0.03832341 0.0004022662
## 58      1 0.0014174742 0.03220140 0.2154357 0.02480948 0.0007105204 0.03829259 0.0004006920
## 59      1 0.0014849683 0.03222194 0.2150086 0.02483081 0.0007068315 0.03826990 0.0003998271
## 60      1 0.0015556761 0.03224445 0.2145226 0.02485464 0.0007039670 0.03825033 0.0003987774
## 61      1 0.0016297508 0.03226926 0.2139634 0.02488105 0.0007011324 0.03822533 0.0003975780
## 62      1 0.0017073526 0.03229652 0.2133225 0.02490917 0.0006981089 0.03817832 0.0003958059
## 63      1 0.0017886495 0.03232636 0.2125956 0.02493918 0.0006949747 0.03811556 0.0003944498
## 64      1 0.0018738174 0.03235829 0.2118186 0.02497095 0.0006928792 0.03800505 0.0003932537
## 65      1 0.0019630407 0.03239219 0.2110041 0.02500403 0.0006913812 0.03789463 0.0003912399
## 66      1 0.0020565123 0.03242568 0.2103095 0.02503698 0.0006905742 0.03782107 0.0003893355
## 67      1 0.0021544347 0.03246075 0.2096169 0.02507189 0.0006906585 0.03767787 0.0003879456
## 68      1 0.0022570197 0.03249606 0.2090355 0.02510712 0.0006899262 0.03757777 0.0003860563
## 69      1 0.0023644894 0.03253415 0.2084098 0.02514434 0.0006895135 0.03745045 0.0003843998
## 70      1 0.0024770764 0.03257588 0.2076910 0.02518442 0.0006893481 0.03730462 0.0003830127
## 71      1 0.0025950242 0.03262162 0.2068602 0.02522766 0.0006894645 0.03713652 0.0003820396
## 72      1 0.0027185882 0.03267174 0.2058957 0.02527416 0.0006899028 0.03694181 0.0003820368
## 73      1 0.0028480359 0.03272666 0.2047718 0.02532376 0.0006907088 0.03671547 0.0003825903
## 74      1 0.0029836472 0.03278684 0.2034570 0.02537698 0.0006919327 0.03645137 0.0003838695
## 75      1 0.0031257158 0.03285276 0.2019130 0.02543448 0.0006936289 0.03614201 0.0003855535
## 76      1 0.0032745492 0.03292496 0.2000921 0.02549745 0.0006958566 0.03577825 0.0003875407
## 77      1 0.0034304693 0.03300402 0.1979353 0.02556541 0.0006986792 0.03534887 0.0003908716
## 78      1 0.0035938137 0.03309058 0.1953695 0.02563875 0.0007021645 0.03484016 0.0003950751
## 79      1 0.0037649358 0.03318528 0.1923058 0.02571821 0.0007063783 0.03423995 0.0004012024
## 80      1 0.0039442061 0.03328586 0.1889009 0.02580270 0.0007103680 0.03364602 0.0004077014
## 81      1 0.0041320124 0.03339347 0.1850321 0.02589114 0.0007153055 0.03317041 0.0004140269
## 82      1 0.0043287613 0.03349602 0.1818112 0.02597489 0.0007152004 0.03295653 0.0004154521
## 83      1 0.0045348785 0.03360379 0.1783076 0.02606287 0.0007170796 0.03240156 0.0004179803
## 84      1 0.0047508102 0.03372085 0.1740859 0.02615709 0.0007204269 0.03173004 0.0004213301
## 85      1 0.0049770236 0.03384857 0.1688900 0.02625893 0.0007245589 0.03089707 0.0004271334
## 86      1 0.0052140083 0.03398754 0.1624760 0.02636955 0.0007300151 0.02978543 0.0004353377
## 87      1 0.0054622772 0.03413695 0.1547476 0.02648772 0.0007375872 0.02857546 0.0004451220
## 88      1 0.0057223677 0.03428323 0.1470087 0.02660214 0.0007442228 0.02716279 0.0004566132
## 89      1 0.0059948425 0.03443218 0.1385423 0.02671791 0.0007550701 0.02533534 0.0004708915
## 90      1 0.0062802914 0.03456278 0.1319602 0.02681402 0.0007611921 0.02463343 0.0004809028
## 91      1 0.0065793322 0.03469603 0.1247634 0.02690998 0.0007692642 0.02422339 0.0004918811
## 92      1 0.0068926121 0.03482128 0.1184698 0.02699800 0.0007718331 0.02491174 0.0004953887
## 93      1 0.0072208090 0.03495233 0.1109458 0.02709032 0.0007779862 0.02530549 0.0004996236
## 94      1 0.0075646333 0.03505674 0.1068584 0.02716450 0.0007804892 0.02476156 0.0005034510
## 95      1 0.0079248290 0.03515278 0.1042371 0.02723276 0.0007920608 0.02329182 0.0005120963
## 96      1 0.0083021757 0.03524229 0.1038025 0.02729509 0.0007990456 0.02345731 0.0005188893
## 97      1 0.0086974900 0.03533734 0.1038025 0.02736183 0.0008080099 0.02345731 0.0005273361
## 98      1 0.0091116276 0.03544136 0.1038025 0.02743474 0.0008175321 0.02345731 0.0005364083
## 99      1 0.0095454846 0.03555519 0.1038025 0.02751488 0.0008276366 0.02345731 0.0005445086
## 100     1 0.0100000000 0.03567970 0.1038025 0.02760324 0.0008383470 0.02345731 0.0005521625

## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

## [1] "Coefficients"
##                model.coef
## (Intercept)  1.999620e+00
## x4          -3.192729e-05
## x5           1.298986e-04
## x7           1.026337e-02
## x8           2.468266e-04
## x9           2.854969e-03
## x10          7.169840e-04
## x11          6.360430e+04
## x14         -9.023026e-06
## x16          4.469093e-04
## x17          1.098423e-03
## x19          1.193228e-05
## x21          6.167787e-05
## x22         -7.402228e-06
## stat3        4.051790e-05
## stat4       -6.713828e-05
## stat13      -3.091034e-04
## stat14      -3.997486e-04
## stat15      -1.691767e-05
## stat22      -2.998355e-04
## stat23       4.173617e-04
## stat24      -3.792153e-04
## stat25      -7.594691e-05
## stat26      -5.072840e-06
## stat30       4.589487e-05
## stat35      -4.278460e-05
## stat37      -9.091416e-05
## stat38       8.747548e-05
## stat39      -4.550145e-05
## stat41      -1.986573e-04
## stat43      -4.992256e-05
## stat45      -2.277058e-06
## stat50       8.465589e-05
## stat51       1.792312e-04
## stat54      -8.773038e-05
## stat55       2.978606e-05
## stat59       8.998934e-05
## stat60       8.193966e-05
## stat63       1.061022e-04
## stat65      -9.633573e-06
## stat75      -8.206138e-07
## stat87      -1.393615e-04
## stat91      -8.354389e-05
## stat92      -2.171178e-04
## stat94      -3.246685e-05
## stat95      -1.720130e-04
## stat98       3.231148e-03
## stat99       1.796786e-05
## stat100      2.543515e-04
## stat104     -5.513857e-05
## stat106     -1.797958e-04
## stat110     -2.978722e-03
## stat112     -8.945143e-06
## stat113     -1.452536e-05
## stat115      6.441635e-06
## stat130      5.114863e-05
## stat144      2.686242e-04
## stat146     -1.326285e-04
## stat147     -6.098621e-05
## stat149     -2.858630e-04
## stat152     -1.508949e-05
## stat156      1.688586e-04
## stat170     -1.565258e-04
## stat172      8.751617e-05
## stat173     -1.979953e-05
## stat175     -1.686258e-04
## stat185     -7.067548e-05
## stat187     -1.034201e-04
## stat191     -1.990295e-05
## stat199      4.584725e-05
## stat204     -1.391253e-04
## stat207      1.668615e-05
## stat210     -1.210908e-05
## stat214     -2.243818e-05
## stat217      3.725489e-05
## x18.sqrt     2.409284e-02

======= ## 0.0001000000 0.03186254 0.2131706 0.02448446 ## 0.0001047616 0.03185287 0.2135421 0.02447754 ## 0.0001097499 0.03184290 0.2139273 0.02447050 ## 0.0001149757 0.03183278 0.2143197 0.02446345 ## 0.0001204504 0.03182251 0.2147196 0.02445629 ## 0.0001261857 0.03181203 0.2151295 0.02444900 ## 0.0001321941 0.03180124 0.2155546 0.02444145 ## 0.0001384886 0.03179022 0.2159929 0.02443365 ## 0.0001450829 0.03177900 0.2164424 0.02442555 ## 0.0001519911 0.03176751 0.2169073 0.02441716 ## 0.0001592283 0.03175573 0.2173883 0.02440850 ## 0.0001668101 0.03174379 0.2178795 0.02439969 ## 0.0001747528 0.03173156 0.2183867 0.02439073 ## 0.0001830738 0.03171937 0.2188955 0.02438193 ## 0.0001917910 0.03170710 0.2194114 0.02437324 ## 0.0002009233 0.03169455 0.2199451 0.02436448 ## 0.0002104904 0.03168172 0.2204961 0.02435570 ## 0.0002205131 0.03166879 0.2210587 0.02434699 ## 0.0002310130 0.03165573 0.2216326 0.02433833 ## 0.0002420128 0.03164269 0.2222132 0.02432989 ## 0.0002535364 0.03162937 0.2228143 0.02432140 ## 0.0002656088 0.03161609 0.2234218 0.02431286 ## 0.0002782559 0.03160254 0.2240509 0.02430405 ## 0.0002915053 0.03158888 0.2246960 0.02429503 ## 0.0003053856 0.03157553 0.2253375 0.02428615 ## 0.0003199267 0.03156213 0.2259943 0.02427741 ## 0.0003351603 0.03154912 0.2266462 0.02426905 ## 0.0003511192 0.03153688 0.2272725 0.02426095 ## 0.0003678380 0.03152472 0.2279069 0.02425278 ## 0.0003853529 0.03151364 0.2285015 0.02424530 ## 0.0004037017 0.03150354 0.2290623 0.02423817 ## 0.0004229243 0.03149441 0.2295903 0.02423105 ## 0.0004430621 0.03148657 0.2300705 0.02422479 ## 0.0004641589 0.03148012 0.2304946 0.02421964 ## 0.0004862602 0.03147502 0.2308656 0.02421592 ## 0.0005094138 0.03147118 0.2311882 0.02421398 ## 0.0005336699 0.03146793 0.2314971 0.02421329 ## 0.0005590810 0.03146563 0.2317725 0.02421364 ## 0.0005857021 0.03146485 0.2319857 0.02421510 ## 0.0006135907 0.03146584 0.2321220 0.02421818 ## 0.0006428073 0.03146918 0.2321489 0.02422348 ## 0.0006734151 0.03147475 0.2320748 0.02423001 ## 0.0007054802 0.03148285 0.2318850 0.02423797 ## 0.0007390722 0.03149216 0.2316487 0.02424663 ## 0.0007742637 0.03150352 0.2313229 0.02425721 ## 0.0008111308 0.03151561 0.2309812 0.02426887 ## 0.0008497534 0.03152883 0.2306043 0.02428169 ## 0.0008902151 0.03154318 0.2301866 0.02429514 ## 0.0009326033 0.03155801 0.2297646 0.02430946 ## 0.0009770100 0.03157373 0.2293186 0.02432425 ## 0.0010235310 0.03159029 0.2288493 0.02433989 ## 0.0010722672 0.03160905 0.2282867 0.02435774 ## 0.0011233240 0.03162880 0.2276984 0.02437730 ## 0.0011768120 0.03164967 0.2270796 0.02439749 ## 0.0012328467 0.03167075 0.2264811 0.02441810 ## 0.0012915497 0.03169277 0.2258702 0.02443960 ## 0.0013530478 0.03171508 0.2252849 0.02446178 ## 0.0014174742 0.03173903 0.2246526 0.02448601 ## 0.0014849683 0.03176478 0.2239701 0.02451191 ## 0.0015556761 0.03179265 0.2232226 0.02454013 ## 0.0016297508 0.03182310 0.2223846 0.02457066 ## 0.0017073526 0.03185634 0.2214465 0.02460369 ## 0.0017886495 0.03189252 0.2203999 0.02463923 ## 0.0018738174 0.03193174 0.2192377 0.02467710 ## 0.0019630407 0.03197388 0.2179690 0.02471746 ## 0.0020565123 0.03201695 0.2167355 0.02475935 ## 0.0021544347 0.03205945 0.2156429 0.02480038 ## 0.0022570197 0.03210426 0.2145055 0.02484348 ## 0.0023644894 0.03215061 0.2133777 0.02488785 ## 0.0024770764 0.03219908 0.2122371 0.02493429 ## 0.0025950242 0.03224814 0.2111939 0.02498085 ## 0.0027185882 0.03230077 0.2100683 0.02502947 ## 0.0028480359 0.03235759 0.2088192 0.02508109 ## 0.0029836472 0.03241976 0.2073653 0.02513682 ## 0.0031257158 0.03248784 0.2056592 0.02519677 ## 0.0032745492 0.03256239 0.2036489 0.02526150 ## 0.0034304693 0.03264401 0.2012711 0.02533115 ## 0.0035938137 0.03273121 0.1986201 0.02540430 ## 0.0037649358 0.03282229 0.1958230 0.02548042 ## 0.0039442061 0.03291521 0.1930845 0.02555791 ## 0.0041320124 0.03300820 0.1905777 0.02563477 ## 0.0043287613 0.03310881 0.1876581 0.02571685 ## 0.0045348785 0.03321832 0.1841423 0.02580479 ## 0.0047508102 0.03333808 0.1798125 0.02589992 ## 0.0049770236 0.03346901 0.1744487 0.02600325 ## 0.0052140083 0.03361185 0.1677970 0.02611460 ## 0.0054622772 0.03376758 0.1595180 0.02623513 ## 0.0057223677 0.03392750 0.1503030 0.02635743 ## 0.0059948425 0.03408432 0.1407341 0.02647539 ## 0.0062802914 0.03422971 0.1321208 0.02658008 ## 0.0065793322 0.03435491 0.1254670 0.02666645 ## 0.0068926121 0.03447684 0.1190162 0.02675022 ## 0.0072208090 0.03459142 0.1131615 0.02682868 ## 0.0075646333 0.03469121 0.1096721 0.02689845 ## 0.0079248290 0.03477185 0.1096415 0.02695410 ## 0.0083021757 0.03486007 0.1096104 0.02701474 ## 0.0086974900 0.03495639 0.1096104 0.02708170 ## 0.0091116276 0.03506180 0.1096104 0.02715569 ## 0.0095454846 0.03517711 0.1096104 0.02723706 ## 0.0100000000 0.03530321 0.1096104 0.02732657 ## ## Tuning parameter 'alpha' was held constant at a value of 1 ## RMSE was used to select the optimal model using the smallest value. ## The final values used for the model were alpha = 1 and lambda = 0.0005857021.

##    alpha       lambda
## 39     1 0.0005857021
##     alpha       lambda       RMSE  Rsquared        MAE       RMSESD RsquaredSD        MAESD
## 1       1 0.0001000000 0.03186254 0.2131706 0.02448446 0.0010816415 0.03059149 0.0006225145
## 2       1 0.0001047616 0.03185287 0.2135421 0.02447754 0.0010806578 0.03061109 0.0006218163
## 3       1 0.0001097499 0.03184290 0.2139273 0.02447050 0.0010796780 0.03063311 0.0006210306
## 4       1 0.0001149757 0.03183278 0.2143197 0.02446345 0.0010786347 0.03065167 0.0006199662
## 5       1 0.0001204504 0.03182251 0.2147196 0.02445629 0.0010776461 0.03067391 0.0006186734
## 6       1 0.0001261857 0.03181203 0.2151295 0.02444900 0.0010765133 0.03068742 0.0006171169
## 7       1 0.0001321941 0.03180124 0.2155546 0.02444145 0.0010753657 0.03069829 0.0006153765
## 8       1 0.0001384886 0.03179022 0.2159929 0.02443365 0.0010742877 0.03071623 0.0006136614
## 9       1 0.0001450829 0.03177900 0.2164424 0.02442555 0.0010733520 0.03074157 0.0006120619
## 10      1 0.0001519911 0.03176751 0.2169073 0.02441716 0.0010724554 0.03077286 0.0006105353
## 11      1 0.0001592283 0.03175573 0.2173883 0.02440850 0.0010715325 0.03080546 0.0006088284
## 12      1 0.0001668101 0.03174379 0.2178795 0.02439969 0.0010706120 0.03083976 0.0006070682
## 13      1 0.0001747528 0.03173156 0.2183867 0.02439073 0.0010698246 0.03087357 0.0006055616
## 14      1 0.0001830738 0.03171937 0.2188955 0.02438193 0.0010688719 0.03089765 0.0006041654
## 15      1 0.0001917910 0.03170710 0.2194114 0.02437324 0.0010678191 0.03091850 0.0006029665
## 16      1 0.0002009233 0.03169455 0.2199451 0.02436448 0.0010668853 0.03095159 0.0006021066
## 17      1 0.0002104904 0.03168172 0.2204961 0.02435570 0.0010658951 0.03098268 0.0006015381
## 18      1 0.0002205131 0.03166879 0.2210587 0.02434699 0.0010648152 0.03101650 0.0006008219
## 19      1 0.0002310130 0.03165573 0.2216326 0.02433833 0.0010636070 0.03104953 0.0006002490
## 20      1 0.0002420128 0.03164269 0.2222132 0.02432989 0.0010617190 0.03106049 0.0005990607
## 21      1 0.0002535364 0.03162937 0.2228143 0.02432140 0.0010592583 0.03105938 0.0005977307
## 22      1 0.0002656088 0.03161609 0.2234218 0.02431286 0.0010562568 0.03103555 0.0005956924
## 23      1 0.0002782559 0.03160254 0.2240509 0.02430405 0.0010526590 0.03099020 0.0005927604
## 24      1 0.0002915053 0.03158888 0.2246960 0.02429503 0.0010489110 0.03095464 0.0005896721
## 25      1 0.0003053856 0.03157553 0.2253375 0.02428615 0.0010451476 0.03093785 0.0005862107
## 26      1 0.0003199267 0.03156213 0.2259943 0.02427741 0.0010413014 0.03094294 0.0005820946
## 27      1 0.0003351603 0.03154912 0.2266462 0.02426905 0.0010376769 0.03098014 0.0005777432
## 28      1 0.0003511192 0.03153688 0.2272725 0.02426095 0.0010334578 0.03098666 0.0005728602
## 29      1 0.0003678380 0.03152472 0.2279069 0.02425278 0.0010289148 0.03097041 0.0005677343
## 30      1 0.0003853529 0.03151364 0.2285015 0.02424530 0.0010236841 0.03092529 0.0005627201
## 31      1 0.0004037017 0.03150354 0.2290623 0.02423817 0.0010177993 0.03086858 0.0005578103
## 32      1 0.0004229243 0.03149441 0.2295903 0.02423105 0.0010120648 0.03082125 0.0005527572
## 33      1 0.0004430621 0.03148657 0.2300705 0.02422479 0.0010065515 0.03078805 0.0005477771
## 34      1 0.0004641589 0.03148012 0.2304946 0.02421964 0.0010010731 0.03074240 0.0005431649
## 35      1 0.0004862602 0.03147502 0.2308656 0.02421592 0.0009959623 0.03070814 0.0005390395
## 36      1 0.0005094138 0.03147118 0.2311882 0.02421398 0.0009907084 0.03064639 0.0005349833
## 37      1 0.0005336699 0.03146793 0.2314971 0.02421329 0.0009852179 0.03054176 0.0005307681
## 38      1 0.0005590810 0.03146563 0.2317725 0.02421364 0.0009798335 0.03044806 0.0005266810
## 39      1 0.0005857021 0.03146485 0.2319857 0.02421510 0.0009744800 0.03038492 0.0005225261
## 40      1 0.0006135907 0.03146584 0.2321220 0.02421818 0.0009691706 0.03032166 0.0005183409
## 41      1 0.0006428073 0.03146918 0.2321489 0.02422348 0.0009632859 0.03026012 0.0005132814
## 42      1 0.0006734151 0.03147475 0.2320748 0.02423001 0.0009574506 0.03018704 0.0005083421
## 43      1 0.0007054802 0.03148285 0.2318850 0.02423797 0.0009522075 0.03013845 0.0005032098
## 44      1 0.0007390722 0.03149216 0.2316487 0.02424663 0.0009476385 0.03013464 0.0004984777
## 45      1 0.0007742637 0.03150352 0.2313229 0.02425721 0.0009443090 0.03019861 0.0004934302
## 46      1 0.0008111308 0.03151561 0.2309812 0.02426887 0.0009410966 0.03032250 0.0004889598
## 47      1 0.0008497534 0.03152883 0.2306043 0.02428169 0.0009375036 0.03047281 0.0004844285
## 48      1 0.0008902151 0.03154318 0.2301866 0.02429514 0.0009340251 0.03063555 0.0004808780
## 49      1 0.0009326033 0.03155801 0.2297646 0.02430946 0.0009300631 0.03076275 0.0004771733
## 50      1 0.0009770100 0.03157373 0.2293186 0.02432425 0.0009261764 0.03091865 0.0004739790
## 51      1 0.0010235310 0.03159029 0.2288493 0.02433989 0.0009219009 0.03106193 0.0004710222
## 52      1 0.0010722672 0.03160905 0.2282867 0.02435774 0.0009176930 0.03119991 0.0004682422
## 53      1 0.0011233240 0.03162880 0.2276984 0.02437730 0.0009139692 0.03128803 0.0004668880
## 54      1 0.0011768120 0.03164967 0.2270796 0.02439749 0.0009106334 0.03141549 0.0004658644
## 55      1 0.0012328467 0.03167075 0.2264811 0.02441810 0.0009069274 0.03144445 0.0004652042
## 56      1 0.0012915497 0.03169277 0.2258702 0.02443960 0.0009032899 0.03151830 0.0004648124
## 57      1 0.0013530478 0.03171508 0.2252849 0.02446178 0.0008991696 0.03153616 0.0004641038
## 58      1 0.0014174742 0.03173903 0.2246526 0.02448601 0.0008958252 0.03158916 0.0004636912
## 59      1 0.0014849683 0.03176478 0.2239701 0.02451191 0.0008931801 0.03166195 0.0004638868
## 60      1 0.0015556761 0.03179265 0.2232226 0.02454013 0.0008910066 0.03177314 0.0004646398
## 61      1 0.0016297508 0.03182310 0.2223846 0.02457066 0.0008892402 0.03190584 0.0004657213
## 62      1 0.0017073526 0.03185634 0.2214465 0.02460369 0.0008873051 0.03205254 0.0004670256
## 63      1 0.0017886495 0.03189252 0.2203999 0.02463923 0.0008852125 0.03221355 0.0004684890
## 64      1 0.0018738174 0.03193174 0.2192377 0.02467710 0.0008828851 0.03237307 0.0004700008
## 65      1 0.0019630407 0.03197388 0.2179690 0.02471746 0.0008803235 0.03251003 0.0004720877
## 66      1 0.0020565123 0.03201695 0.2167355 0.02475935 0.0008782437 0.03276090 0.0004736465
## 67      1 0.0021544347 0.03205945 0.2156429 0.02480038 0.0008755669 0.03286425 0.0004741269
## 68      1 0.0022570197 0.03210426 0.2145055 0.02484348 0.0008731160 0.03303330 0.0004740046
## 69      1 0.0023644894 0.03215061 0.2133777 0.02488785 0.0008697195 0.03312975 0.0004728314
## 70      1 0.0024770764 0.03219908 0.2122371 0.02493429 0.0008666542 0.03329081 0.0004716820
## 71      1 0.0025950242 0.03224814 0.2111939 0.02498085 0.0008627554 0.03330024 0.0004694517
## 72      1 0.0027185882 0.03230077 0.2100683 0.02502947 0.0008590609 0.03337342 0.0004680067
## 73      1 0.0028480359 0.03235759 0.2088192 0.02508109 0.0008551360 0.03346376 0.0004670723
## 74      1 0.0029836472 0.03241976 0.2073653 0.02513682 0.0008510986 0.03356231 0.0004665059
## 75      1 0.0031257158 0.03248784 0.2056592 0.02519677 0.0008469106 0.03365733 0.0004664300
## 76      1 0.0032745492 0.03256239 0.2036489 0.02526150 0.0008425703 0.03374455 0.0004658111
## 77      1 0.0034304693 0.03264401 0.2012711 0.02533115 0.0008380791 0.03381881 0.0004646748
## 78      1 0.0035938137 0.03273121 0.1986201 0.02540430 0.0008331604 0.03388408 0.0004636922
## 79      1 0.0037649358 0.03282229 0.1958230 0.02548042 0.0008284423 0.03374588 0.0004622902
## 80      1 0.0039442061 0.03291521 0.1930845 0.02555791 0.0008251746 0.03388233 0.0004636622
## 81      1 0.0041320124 0.03300820 0.1905777 0.02563477 0.0008214935 0.03375383 0.0004640136
## 82      1 0.0043287613 0.03310881 0.1876581 0.02571685 0.0008184043 0.03375498 0.0004644003
## 83      1 0.0045348785 0.03321832 0.1841423 0.02580479 0.0008151915 0.03372051 0.0004639725
## 84      1 0.0047508102 0.03333808 0.1798125 0.02589992 0.0008120953 0.03362327 0.0004642206
## 85      1 0.0049770236 0.03346901 0.1744487 0.02600325 0.0008091510 0.03343275 0.0004620281
## 86      1 0.0052140083 0.03361185 0.1677970 0.02611460 0.0008057895 0.03308994 0.0004578725
## 87      1 0.0054622772 0.03376758 0.1595180 0.02623513 0.0008018740 0.03251782 0.0004509641
## 88      1 0.0057223677 0.03392750 0.1503030 0.02635743 0.0007921065 0.03163494 0.0004389589
## 89      1 0.0059948425 0.03408432 0.1407341 0.02647539 0.0007728687 0.02915934 0.0004206739
## 90      1 0.0062802914 0.03422971 0.1321208 0.02658008 0.0007598752 0.02873562 0.0004091920
## 91      1 0.0065793322 0.03435491 0.1254670 0.02666645 0.0007483329 0.02662652 0.0004003342
## 92      1 0.0068926121 0.03447684 0.1190162 0.02675022 0.0007397248 0.02574520 0.0003921189
## 93      1 0.0072208090 0.03459142 0.1131615 0.02682868 0.0007368861 0.02372812 0.0003850593
## 94      1 0.0075646333 0.03469121 0.1096721 0.02689845 0.0007358720 0.02471483 0.0003812929
## 95      1 0.0079248290 0.03477185 0.1096415 0.02695410 0.0007343381 0.02475087 0.0003794832
## 96      1 0.0083021757 0.03486007 0.1096104 0.02701474 0.0007329875 0.02478797 0.0003777373
## 97      1 0.0086974900 0.03495639 0.1096104 0.02708170 0.0007316796 0.02478797 0.0003770035
## 98      1 0.0091116276 0.03506180 0.1096104 0.02715569 0.0007307107 0.02478797 0.0003774184
## 99      1 0.0095454846 0.03517711 0.1096104 0.02723706 0.0007301431 0.02478797 0.0003791633
## 100     1 0.0100000000 0.03530321 0.1096104 0.02732657 0.0007300461 0.02478797 0.0003835752

## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

## [1] "Coefficients"
##                model.coef
## (Intercept)  1.993238e+00
## x4          -3.322227e-05
## x7           9.914108e-03
## x8           2.584645e-04
## x9           2.633861e-03
## x10          7.245818e-04
## x11          1.061230e+05
## x14         -1.134113e-05
## x16          7.740589e-04
## x17          1.423644e-03
## x21          4.028261e-05
## stat3        1.094643e-04
## stat4       -2.159159e-04
## stat10      -4.625205e-07
## stat13      -3.488169e-04
## stat14      -3.898007e-04
## stat18      -3.075583e-06
## stat22      -1.343960e-04
## stat23       2.165912e-04
## stat24      -1.745584e-04
## stat25      -2.026026e-04
## stat26      -5.461865e-05
## stat33      -6.567348e-05
## stat35      -2.033416e-05
## stat38       4.163937e-05
## stat41      -3.859030e-04
## stat45      -3.866762e-05
## stat48       8.810615e-06
## stat54      -1.757184e-07
## stat59       7.866764e-05
## stat60       8.085970e-06
## stat65      -1.834546e-04
## stat70       4.300945e-05
## stat73       3.196639e-05
## stat86       3.758349e-05
## stat89      -7.070199e-06
## stat91      -1.266341e-04
## stat96      -4.010251e-07
## stat98       3.235892e-03
## stat100      1.147835e-04
## stat110     -3.080214e-03
## stat130      1.815544e-04
## stat144      2.632748e-04
## stat146     -2.296307e-04
## stat147     -1.889099e-06
## stat149     -1.792711e-04
## stat156      7.789184e-05
## stat166     -5.466565e-05
## stat175     -1.862416e-04
## stat180     -1.663797e-04
## stat198     -6.511567e-08
## stat204     -1.922317e-04
## stat207      5.226865e-05
## stat213     -2.276448e-05
## stat214     -2.622186e-05
## x18.sqrt     2.456374e-02

>>>>>>> 8e6f61bca4894b586983e20a3e14b1b8a049b903

Test

if (algo.LASSO.caret == TRUE){
  test.model(model.LASSO.caret, data.test
             ,method = 'glmnet',subopt = "LASSO"
             ,formula = formula, feature.names = feature.names, label.names = label.names
             ,draw.limits = TRUE, transformation = t)
}

## [1] "Summary of predicted values: "
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
<<<<<<< HEAD
##   2.041   2.085   2.097   2.097   2.108   2.148 
## [1] "glmnet LASSO Test MSE: 0.000942657388743223"

======= ## 2.042 2.085 2.097 2.097 2.108 2.139 ## [1] "glmnet LASSO Test MSE: 0.00104739061360084"

>>>>>>> 8e6f61bca4894b586983e20a3e14b1b8a049b903

LARS with CV

Train

if (algo.LARS.caret == TRUE){
  set.seed(1)
  returned = train.caret.glmselect(formula = formula
                                   ,data =  data.train
                                   ,method = "lars"
                                   ,subopt = 'NULL'
                                   ,feature.names = feature.names)
  model.LARS.caret = returned$model
}

## Warning in nominalTrainWorkflow(x = x, y = y, wts = weights, info = trainInfo, : There were missing values in resampled
## performance measures.

## Aggregating results
## Selecting tuning parameters
## Fitting fraction = 0.384 on full training set
## Least Angle Regression 
## 
## 5584 samples
##  240 predictor
## 
## Pre-processing: centered (240), scaled (240) 
## Resampling: Cross-Validated (10 fold) 
## Summary of sample sizes: 5026, 5026, 5026, 5025, 5025, 5026, ... 
## Resampling results across tuning parameters:
## 
##   fraction    RMSE        Rsquared   MAE       
<<<<<<< HEAD
##   0.00000000  0.03615283        NaN  0.02793755
##   0.01010101  0.03573595  0.1038025  0.02764360
##   0.02020202  0.03536764  0.1038025  0.02738318
##   0.03030303  0.03505460  0.1052881  0.02716424
##   0.04040404  0.03477639  0.1206858  0.02696601
##   0.05050505  0.03452627  0.1332179  0.02678628
##   0.06060606  0.03429091  0.1462363  0.02660741
##   0.07070707  0.03407398  0.1582559  0.02643766
##   0.08080808  0.03386395  0.1684154  0.02627123
##   0.09090909  0.03366691  0.1762344  0.02611440
##   0.10101010  0.03348307  0.1822212  0.02596501
##   0.11111111  0.03331393  0.1878454  0.02582624
##   0.12121212  0.03315406  0.1934511  0.02569254
##   0.13131313  0.03300481  0.1979850  0.02556713
##   0.14141414  0.03286642  0.2016245  0.02544747
##   0.15151515  0.03273902  0.2045335  0.02533540
##   0.16161616  0.03262273  0.2068473  0.02522986
##   0.17171717  0.03251769  0.2086771  0.02512989
##   0.18181818  0.03242686  0.2102334  0.02503952
##   0.19191919  0.03234820  0.2120182  0.02496156
##   0.20202020  0.03227757  0.2136557  0.02489123
##   0.21212121  0.03221744  0.2149915  0.02482799
##   0.22222222  0.03216837  0.2160892  0.02477678
##   0.23232323  0.03213206  0.2169287  0.02474073
##   0.24242424  0.03210360  0.2176151  0.02471342
##   0.25252525  0.03207805  0.2183397  0.02468988
##   0.26262626  0.03205588  0.2189945  0.02467061
##   0.27272727  0.03203816  0.2195049  0.02465462
##   0.28282828  0.03202650  0.2197453  0.02464434
##   0.29292929  0.03201865  0.2198456  0.02463728
##   0.30303030  0.03201193  0.2199464  0.02463065
##   0.31313131  0.03200638  0.2200249  0.02462417
##   0.32323232  0.03200233  0.2200526  0.02461863
##   0.33333333  0.03199927  0.2200467  0.02461418
##   0.34343434  0.03199698  0.2200219  0.02460976
##   0.35353535  0.03199531  0.2199737  0.02460510
##   0.36363636  0.03199431  0.2199048  0.02460115
##   0.37373737  0.03199376  0.2198259  0.02459752
##   0.38383838  0.03199364  0.2197357  0.02459424
##   0.39393939  0.03199404  0.2196243  0.02459155
##   0.40404040  0.03199520  0.2194817  0.02458960
##   0.41414141  0.03199666  0.2193325  0.02458791
##   0.42424242  0.03199854  0.2191689  0.02458667
##   0.43434343  0.03200121  0.2189702  0.02458636
##   0.44444444  0.03200412  0.2187664  0.02458632
##   0.45454545  0.03200662  0.2185890  0.02458684
##   0.46464646  0.03200973  0.2183854  0.02458806
##   0.47474747  0.03201334  0.2181640  0.02458983
##   0.48484848  0.03201747  0.2179225  0.02459174
##   0.49494949  0.03202206  0.2176636  0.02459396
##   0.50505051  0.03202699  0.2173928  0.02459667
##   0.51515152  0.03203189  0.2171270  0.02459951
##   0.52525253  0.03203707  0.2168535  0.02460280
##   0.53535354  0.03204265  0.2165663  0.02460652
##   0.54545455  0.03204834  0.2162800  0.02461058
##   0.55555556  0.03205454  0.2159744  0.02461510
##   0.56565657  0.03206103  0.2156616  0.02461988
##   0.57575758  0.03206734  0.2153615  0.02462474
##   0.58585859  0.03207371  0.2150634  0.02462974
##   0.59595960  0.03208031  0.2147571  0.02463489
##   0.60606061  0.03208718  0.2144434  0.02464022
##   0.61616162  0.03209412  0.2141318  0.02464523
##   0.62626263  0.03210154  0.2138030  0.02465031
##   0.63636364  0.03210961  0.2134474  0.02465578
##   0.64646465  0.03211780  0.2130919  0.02466121
##   0.65656566  0.03212607  0.2127368  0.02466661
##   0.66666667  0.03213448  0.2123796  0.02467199
##   0.67676768  0.03214290  0.2120252  0.02467722
##   0.68686869  0.03215138  0.2116711  0.02468248
##   0.69696970  0.03215990  0.2113191  0.02468776
##   0.70707071  0.03216853  0.2109663  0.02469306
##   0.71717172  0.03217748  0.2106033  0.02469854
##   0.72727273  0.03218650  0.2102415  0.02470396
##   0.73737374  0.03219549  0.2098855  0.02470944
##   0.74747475  0.03220458  0.2095294  0.02471504
##   0.75757576  0.03221380  0.2091706  0.02472046
##   0.76767677  0.03222364  0.2087873  0.02472650
##   0.77777778  0.03223350  0.2084061  0.02473281
##   0.78787879  0.03224373  0.2080129  0.02473949
##   0.79797980  0.03225424  0.2076112  0.02474647
##   0.80808081  0.03226462  0.2072182  0.02475338
##   0.81818182  0.03227524  0.2068195  0.02476080
##   0.82828283  0.03228628  0.2064073  0.02476852
##   0.83838384  0.03229763  0.2059868  0.02477634
##   0.84848485  0.03230932  0.2055568  0.02478439
##   0.85858586  0.03232126  0.2051197  0.02479275
##   0.86868687  0.03233347  0.2046751  0.02480146
##   0.87878788  0.03234573  0.2042320  0.02481032
##   0.88888889  0.03235800  0.2037928  0.02481936
##   0.89898990  0.03237031  0.2033572  0.02482865
##   0.90909091  0.03238276  0.2029196  0.02483809
##   0.91919192  0.03239530  0.2024832  0.02484752
##   0.92929293  0.03240791  0.2020484  0.02485715
##   0.93939394  0.03242076  0.2016072  0.02486700
##   0.94949495  0.03243379  0.2011640  0.02487706
##   0.95959596  0.03244720  0.2007096  0.02488780
##   0.96969697  0.03246083  0.2002492  0.02489874
##   0.97979798  0.03247458  0.1997882  0.02490974
##   0.98989899  0.03248853  0.1993232  0.02492083
##   1.00000000  0.03250253  0.1988622  0.02493193
## 
## RMSE was used to select the optimal model using the smallest value.
## The final value used for the model was fraction = 0.3838384.

##     fraction
## 39 0.3838384

## Warning: Removed 1 rows containing missing values (geom_point).

## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

## [1] "Coefficients"
##            x4            x5            x7            x8            x9           x10           x11           x14 
## -1.531793e-03  1.977061e-04  6.911796e-03  7.247751e-04  3.706721e-03  1.006858e-03  3.800232e-04 -1.011551e-05 
##           x16           x17           x19           x21           x22         stat3         stat4        stat13 
##  9.058036e-04  1.460923e-03  3.862172e-05  6.361488e-04 -4.712600e-06  8.007205e-05 -1.246502e-04 -5.447453e-04 
##        stat14        stat15        stat22        stat23        stat24        stat25        stat26        stat30 
## -7.104915e-04 -3.829481e-05 -5.273807e-04  7.329366e-04 -6.632203e-04 -1.422530e-04 -2.263488e-06  8.680800e-05 
##        stat35        stat37        stat38        stat39        stat41        stat43        stat50        stat51 
## -8.469060e-05 -1.656486e-04  1.616390e-04 -8.751430e-05 -3.525696e-04 -9.516236e-05  1.576032e-04  3.178300e-04 
##        stat54        stat55        stat59        stat60        stat63        stat65        stat87        stat91 
## -1.606147e-04  6.081155e-05  1.619828e-04  1.522761e-04  1.911492e-04 -1.513368e-05 -2.505654e-04 -1.540178e-04 
##        stat92        stat94        stat95        stat98        stat99       stat100       stat104       stat106 
## -3.809821e-04 -6.608045e-05 -3.077679e-04  5.701316e-03  3.993515e-05  4.540061e-04 -1.050582e-04 -3.217559e-04 
##       stat110       stat112       stat113       stat115       stat130       stat144       stat146       stat147 
## -5.161655e-03 -1.570879e-05 -3.178462e-05  8.748157e-06  9.613664e-05  4.754582e-04 -2.384243e-04 -1.153419e-04 
##       stat149       stat152       stat156       stat170       stat172       stat173       stat175       stat185 
## -5.013289e-04 -3.340497e-05  3.000084e-04 -2.786896e-04  1.615455e-04 -4.349482e-05 -3.027524e-04 -1.340565e-04 
##       stat187       stat191       stat199       stat204       stat207       stat210       stat214       stat217 
## -1.897762e-04 -4.377823e-05  9.031433e-05 -2.532868e-04  3.643533e-05 -2.479095e-05 -4.731099e-05  7.200011e-05 
##      x18.sqrt 
##  1.093130e-02

======= ## 0.00000000 0.03585074 NaN 0.02771086 ## 0.01010101 0.03544188 0.1096104 0.02742321 ## 0.02020202 0.03507687 0.1096104 0.02716467 ## 0.03030303 0.03475710 0.1096104 0.02694238 ## 0.04040404 0.03448412 0.1182772 0.02675612 ## 0.05050505 0.03423647 0.1310634 0.02658569 ## 0.06060606 0.03401173 0.1448227 0.02642057 ## 0.07070707 0.03379604 0.1577741 0.02625639 ## 0.08080808 0.03358850 0.1688316 0.02609598 ## 0.09090909 0.03339255 0.1775365 0.02594327 ## 0.10101010 0.03320840 0.1843373 0.02579742 ## 0.11111111 0.03303625 0.1896267 0.02565866 ## 0.12121212 0.03287754 0.1938795 0.02552706 ## 0.13131313 0.03273113 0.1984520 0.02540406 ## 0.14141414 0.03259208 0.2027354 0.02528693 ## 0.15151515 0.03246282 0.2062307 0.02517520 ## 0.16161616 0.03234346 0.2090687 0.02506927 ## 0.17171717 0.03223599 0.2114361 0.02496995 ## 0.18181818 0.03213989 0.2135030 0.02487723 ## 0.19191919 0.03205252 0.2157609 0.02479417 ## 0.20202020 0.03197263 0.2179263 0.02471703 ## 0.21212121 0.03189582 0.2202754 0.02464334 ## 0.22222222 0.03182709 0.2222345 0.02457592 ## 0.23232323 0.03176676 0.2238983 0.02451602 ## 0.24242424 0.03171555 0.2252527 0.02446447 ## 0.25252525 0.03167271 0.2263736 0.02442224 ## 0.26262626 0.03163388 0.2275004 0.02438282 ## 0.27272727 0.03159940 0.2285528 0.02434910 ## 0.28282828 0.03157258 0.2293418 0.02432399 ## 0.29292929 0.03155020 0.2299920 0.02430222 ## 0.30303030 0.03153097 0.2305637 0.02428376 ## 0.31313131 0.03151493 0.2310113 0.02426823 ## 0.32323232 0.03150084 0.2314032 0.02425458 ## 0.33333333 0.03148914 0.2317196 0.02424369 ## 0.34343434 0.03147959 0.2319635 0.02423469 ## 0.35353535 0.03147204 0.2321366 0.02422760 ## 0.36363636 0.03146727 0.2321815 0.02422147 ## 0.37373737 0.03146451 0.2321394 0.02421704 ## 0.38383838 0.03146357 0.2320228 0.02421425 ## 0.39393939 0.03146418 0.2318430 0.02421297 ## 0.40404040 0.03146604 0.2316160 0.02421268 ## 0.41414141 0.03146853 0.2313690 0.02421315 ## 0.42424242 0.03147116 0.2311285 0.02421388 ## 0.43434343 0.03147425 0.2308761 0.02421511 ## 0.44444444 0.03147797 0.2306000 0.02421768 ## 0.45454545 0.03148260 0.2302889 0.02422125 ## 0.46464646 0.03148811 0.2299426 0.02422567 ## 0.47474747 0.03149436 0.2295655 0.02423091 ## 0.48484848 0.03150098 0.2291816 0.02423591 ## 0.49494949 0.03150817 0.2287783 0.02424101 ## 0.50505051 0.03151597 0.2283530 0.02424633 ## 0.51515152 0.03152425 0.2279114 0.02425211 ## 0.52525253 0.03153286 0.2274629 0.02425788 ## 0.53535354 0.03154196 0.2269958 0.02426372 ## 0.54545455 0.03155130 0.2265222 0.02426962 ## 0.55555556 0.03156104 0.2260369 0.02427578 ## 0.56565657 0.03157118 0.2255389 0.02428238 ## 0.57575758 0.03158151 0.2250400 0.02428927 ## 0.58585859 0.03159192 0.2245450 0.02429640 ## 0.59595960 0.03160257 0.2240443 0.02430357 ## 0.60606061 0.03161343 0.2235402 0.02431078 ## 0.61616162 0.03162394 0.2230582 0.02431733 ## 0.62626263 0.03163465 0.2225724 0.02432406 ## 0.63636364 0.03164545 0.2220872 0.02433086 ## 0.64646465 0.03165637 0.2216011 0.02433800 ## 0.65656566 0.03166729 0.2211212 0.02434531 ## 0.66666667 0.03167825 0.2206451 0.02435272 ## 0.67676768 0.03168941 0.2201645 0.02436042 ## 0.68686869 0.03170068 0.2196833 0.02436829 ## 0.69696970 0.03171186 0.2192113 0.02437609 ## 0.70707071 0.03172306 0.2187423 0.02438406 ## 0.71717172 0.03173460 0.2182616 0.02439237 ## 0.72727273 0.03174633 0.2177758 0.02440098 ## 0.73737374 0.03175820 0.2172888 0.02440974 ## 0.74747475 0.03177009 0.2168052 0.02441848 ## 0.75757576 0.03178206 0.2163225 0.02442729 ## 0.76767677 0.03179406 0.2158438 0.02443587 ## 0.77777778 0.03180631 0.2153591 0.02444456 ## 0.78787879 0.03181863 0.2148755 0.02445323 ## 0.79797980 0.03183120 0.2143856 0.02446209 ## 0.80808081 0.03184402 0.2138881 0.02447101 ## 0.81818182 0.03185697 0.2133890 0.02448027 ## 0.82828283 0.03187007 0.2128876 0.02448968 ## 0.83838384 0.03188334 0.2123831 0.02449927 ## 0.84848485 0.03189694 0.2118687 0.02450917 ## 0.85858586 0.03191055 0.2113570 0.02451905 ## 0.86868687 0.03192424 0.2108451 0.02452906 ## 0.87878788 0.03193801 0.2103347 0.02453932 ## 0.88888889 0.03195200 0.2098187 0.02454985 ## 0.89898990 0.03196604 0.2093054 0.02456024 ## 0.90909091 0.03198009 0.2087963 0.02457058 ## 0.91919192 0.03199442 0.2082788 0.02458120 ## 0.92929293 0.03200879 0.2077636 0.02459188 ## 0.93939394 0.03202299 0.2072601 0.02460251 ## 0.94949495 0.03203722 0.2067602 0.02461313 ## 0.95959596 0.03205167 0.2062548 0.02462390 ## 0.96969697 0.03206621 0.2057499 0.02463481 ## 0.97979798 0.03208080 0.2052478 0.02464587 ## 0.98989899 0.03209529 0.2047544 0.02465698 ## 1.00000000 0.03210993 0.2042585 0.02466824 ## ## RMSE was used to select the optimal model using the smallest value. ## The final value used for the model was fraction = 0.3838384.

##     fraction
## 39 0.3838384

## Warning: Removed 1 rows containing missing values (geom_point).

## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

## [1] "Coefficients"
##            x4            x7            x8            x9           x10           x11           x14           x16 
## -1.575481e-03  6.658898e-03  7.387385e-04  3.407229e-03  9.998359e-04  6.115442e-04 -6.635444e-06  1.545808e-03 
##           x17           x21         stat3         stat4        stat13        stat14        stat22        stat23 
##  1.876302e-03  4.007124e-04  1.827028e-04 -3.644477e-04 -6.000876e-04 -6.753247e-04 -2.250790e-04  3.680173e-04 
##        stat24        stat25        stat26        stat33        stat35        stat38        stat41        stat45 
## -2.944903e-04 -3.433677e-04 -8.779615e-05 -1.063788e-04 -2.832547e-05  6.574977e-05 -6.663140e-04 -5.990244e-05 
##        stat48        stat59        stat65        stat70        stat73        stat86        stat91        stat98 
##  6.456400e-06  1.306049e-04 -3.071217e-04  6.779608e-05  4.959550e-05  5.783115e-05 -2.149021e-04  5.670485e-03 
##       stat100       stat110       stat130       stat144       stat146       stat149       stat156       stat166 
##  1.926071e-04 -5.319444e-03  3.100836e-04  4.511700e-04 -3.897256e-04 -3.032107e-04  1.271650e-04 -9.046295e-05 
##       stat175       stat180       stat204       stat207       stat213       stat214      x18.sqrt 
## -3.156293e-04 -2.830228e-04 -3.288871e-04  8.351388e-05 -3.297079e-05 -3.888460e-05  1.118530e-02

>>>>>>> 8e6f61bca4894b586983e20a3e14b1b8a049b903

Test

if (algo.LARS.caret == TRUE){
  test.model(model.LARS.caret, data.test
             ,method = 'lars',subopt = NULL
             ,formula = formula, feature.names = feature.names, label.names = label.names
             ,draw.limits = TRUE, transformation = t)
}

## [1] "Summary of predicted values: "
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
<<<<<<< HEAD
##   2.040   2.085   2.097   2.097   2.108   2.148 
## [1] "lars  Test MSE: 0.000942692945958325"

======= ## 2.042 2.085 2.097 2.097 2.108 2.139 ## [1] "lars Test MSE: 0.00104745935190979"

>>>>>>> 8e6f61bca4894b586983e20a3e14b1b8a049b903

Session Info

sessionInfo()

## R version 3.5.2 (2018-12-20)
## Platform: x86_64-w64-mingw32/x64 (64-bit)
## Running under: Windows Server 2008 R2 x64 (build 7601) Service Pack 1
## 
## Matrix products: default
## 
## locale:
## [1] LC_COLLATE=English_United States.1252  LC_CTYPE=English_United States.1252    LC_MONETARY=English_United States.1252
## [4] LC_NUMERIC=C                           LC_TIME=English_United States.1252    
## 
## attached base packages:
## [1] parallel  stats     graphics  grDevices utils     datasets  methods   base     
## 
## other attached packages:
##  [1] knitr_1.20                 htmltools_0.3.6            reshape2_1.4.3             lars_1.2                  
##  [5] doParallel_1.0.11          iterators_1.0.9            caret_6.0-81               leaps_3.0                 
##  [9] ggforce_0.2.1              rlist_0.4.6.1              car_3.0-2                  carData_3.0-2             
## [13] bestNormalize_1.3.0        scales_1.0.0               onewaytests_2.0            caTools_1.17.1.1          
## [17] mosaic_1.5.0               mosaicData_0.17.0          ggformula_0.9.1            ggstance_0.3.1            
## [21] lattice_0.20-38            DT_0.4                     ggiraphExtra_0.2.9         ggiraph_0.6.0             
## [25] investr_1.4.0              glmnet_2.0-16              foreach_1.4.4              Matrix_1.2-15             
## [29] MASS_7.3-51.1              PerformanceAnalytics_1.5.2 xts_0.10-2                 zoo_1.8-2                 
## [33] forcats_0.3.0              stringr_1.3.1              dplyr_0.8.0.1              purrr_0.2.5               
## [37] readr_1.1.1                tidyr_0.8.1                tibble_2.1.1               ggplot2_3.1.0             
## [41] tidyverse_1.2.1            usdm_1.1-18                raster_2.8-19              sp_1.3-1                  
## [45] pacman_0.5.1              
## 
## loaded via a namespace (and not attached):
##  [1] readxl_1.1.0       backports_1.1.2    plyr_1.8.4         lazyeval_0.2.1     splines_3.5.2      mycor_0.1.1       
##  [7] crosstalk_1.0.0    leaflet_2.0.2      digest_0.6.15      magrittr_1.5       mosaicCore_0.6.0   openxlsx_4.1.0    
## [13] recipes_0.1.4      modelr_0.1.2       gower_0.1.2        colorspace_1.3-2   rvest_0.3.2        ggrepel_0.8.0     
## [19] haven_1.1.2        crayon_1.3.4       jsonlite_1.5       survival_2.43-3    glue_1.3.1         polyclip_1.10-0   
## [25] registry_0.5-1     gtable_0.2.0       ppcor_1.1          ipred_0.9-6        sjmisc_2.7.9       abind_1.4-5       
## [31] rngtools_1.3.1     bibtex_0.4.2       Rcpp_1.0.1         xtable_1.8-2       foreign_0.8-71     stats4_3.5.2      
## [37] lava_1.6.2         prodlim_2018.04.18 htmlwidgets_1.2    httr_1.3.1         RColorBrewer_1.1-2 pkgconfig_2.0.2   
## [43] farver_1.1.0       nnet_7.3-12        labeling_0.3       tidyselect_0.2.5   rlang_0.3.1        later_0.7.3       
## [49] munsell_0.5.0      cellranger_1.1.0   tools_3.5.2        cli_1.0.1          generics_0.0.2     moments_0.14      
## [55] sjlabelled_1.0.17  broom_0.4.5        evaluate_0.10.1    ggdendro_0.1-20    yaml_2.1.19        ModelMetrics_1.1.0
## [61] zip_2.0.1          nlme_3.1-137       doRNG_1.7.1        mime_0.5           xml2_1.2.0         compiler_3.5.2    
## [67] rstudioapi_0.7     curl_3.2           tweenr_1.0.1       stringi_1.2.3      highr_0.7          gdtools_0.1.7     
## [73] psych_1.8.4        pillar_1.3.1       data.table_1.11.4  bitops_1.0-6       insight_0.1.2      httpuv_1.4.4.2    
## [79] R6_2.2.2           promises_1.0.1     gridExtra_2.3      rio_0.5.16         codetools_0.2-15   assertthat_0.2.0  
## [85] pkgmaker_0.27      rprojroot_1.3-2    withr_2.1.2        nortest_1.0-4      mnormt_1.5-5       mgcv_1.8-26       
## [91] hms_0.4.2          quadprog_1.5-5     grid_3.5.2         rpart_4.1-13       timeDate_3043.102  class_7.3-14      
## [97] rmarkdown_1.10     shiny_1.1.0        lubridate_1.7.4